TODCO 12,000,000 Shares* Class A Common Stock (Par Value $0.01 Per Share) Underwriting Agreement

EXHIBIT 1.1

TODCO

12,000,000 Shares*
Class A Common Stock
(Par Value $0.01 Per Share)

Underwriting Agreement

New York, New York
May 13, 2005

Citigroup Global Markets Inc.

Dear Sirs and Mesdames:

     Transocean Inc., a Cayman Islands company (the “Selling Stockholder”), proposes to sell to the several underwriters named in Schedule I hereto (the “Underwriters”) an aggregate of 12,000,000 shares of the Class A common stock (par value $0.01 per share) (the “Firm Shares”) of TODCO, a Delaware corporation (the “Company”).

     The Selling Stockholder also proposes to sell to the several Underwriters not more than an additional 1,310,000 shares of the Class A common stock (par value $0.01 per share) of the Company (the “Additional Shares”) if and to the extent that you, as managers of the offering, shall have determined to exercise, on behalf of the Underwriters, the right to purchase such shares of common stock granted to the Underwriters in Section 3 hereof. The Firm Shares and the Additional Shares are hereinafter collectively referred to as the “Shares.” The shares of Class A common stock (par value $0.01 per share) of the Company to be outstanding after giving effect to the sales contemplated hereby are hereinafter referred to as the “Common Stock.”

     The Company has filed with the Securities and Exchange Commission (the “Commission”) a registration statement, including a prospectus, relating to the Shares. The registration statement as amended at the time it became effective, including the

information (if any) deemed to be part of the registration statement at the time of effectiveness pursuant to Rule 430A under the Securities Act of 1933, as amended (the “Securities Act”), is hereinafter referred to as the “Registration Statement”; the prospectus in the form first used to confirm sales of Shares including any documents incorporated therein or deemed to be incorporated therein is hereinafter referred to as the “Prospectus.” If the Company has filed an abbreviated registration statement to register additional shares of Common Stock pursuant to Rule 462(b) under the Securities Act (the “Rule 462 Registration Statement”), then any reference herein to the term “Registration Statement” shall be deemed to include such Rule 462 Registration Statement.

     1. Representations and Warranties of the Company. The Company represents and warrants to and agrees with each of the Underwriters that:

     (a) The Registration Statement (excluding for this purpose any Rule 462 Registration Statement) has become effective; no stop order suspending the effectiveness of the Registration Statement is in effect, and no proceedings for such purpose are pending before or threatened by the Commission.

     (b) (i) The Registration Statement, when it became effective, did not contain and, as amended or supplemented, if applicable, will not contain any untrue statement of a material fact or omit to state a material fact required to be stated therein or necessary to make the statements therein not misleading, (ii) the Registration Statement and the Prospectus comply and, as amended or supplemented, if applicable, will comply in all material respects with the Securities Act and the applicable rules and regulations of the Commission thereunder and (iii) the Prospectus does not contain and, as amended or supplemented, if applicable, will not contain any untrue statement of a material fact or omit to state a material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading, except that the representations and warranties set forth in this paragraph (b) do not apply to statements or omissions in the Registration Statement or the Prospectus based upon information furnished to the Company in writing by any Underwriter through you expressly for use therein.

     (c) There has not occurred any material adverse change, or any development involving a prospective material adverse change, in the general affairs, management, financial position, stockholders’ equity or result of operations, or in the earnings, business or operations of the Company and its subsidiaries, taken as a whole, from that set forth in the Prospectus (exclusive of any amendments or supplements thereto subsequent to the date of this Agreement).

     (d) The preliminary prospectus supplement dated May 11, 2005 filed pursuant to Rule 424 under the Securities Act, complied when so filed in all

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material respects with the Securities Act and the applicable rules and regulations of the Commission thereunder.

     (e) The statements set forth in the Company’s registration statement on Form 8-A filed with the Commission on February 5, 2004 under the caption “Description of Registrant’s Securities to be Registered” incorporated into the Prospectus, insofar as they purport to constitute a summary of the terms of the Company’s capital stock and the statements set forth in the Prospectus under the caption “Underwriters”, insofar as they purport to describe the provisions of the laws and documents referred to therein, are accurate, complete and fair in all material respects.

     (f) To the knowledge of the Company, Ernst & Young LLP, who have certified certain financial statements of the Company, are independent public accountants as required by the Securities Act and the rules and regulations of the Commission thereunder.

     (g) Each of the Company and its significant subsidiaries (as defined in Rule 1-02(w) forming part of Regulation S-X under the Securities Act, except that the determination of whether a subsidiary is a significant subsidiary shall be made as of the date hereof or as of the Closing Date, as applicable, rather than as of the end of the relevant fiscal year) (each, a “Significant Subsidiary”) has been duly organized and is validly existing as a corporation in good standing under the laws of its jurisdiction of incorporation, with power and authority (corporate and other) to own its properties and conduct its business as described in the Prospectus, and has been duly qualified as a foreign corporation for the transaction of business and is in good standing under the laws of each other jurisdiction in which it owns or leases properties, or conducts any business, so as to require such qualification, except where the failure to be so qualified would not have a material adverse effect on the general affairs, management, financial position, stockholders’ equity or results of operations of the Company and its subsidiaries considered as one enterprise (a “Material Adverse Effect”).

     (h) This Agreement has been duly authorized, executed and delivered by the Company and constitutes a valid and binding agreement of the Company.

     (i) On the Closing Date (as defined in Section 5 hereof), the Company will have an authorized capitalization as set forth in the Prospectus, and all of the outstanding shares of capital stock of the Company (including the Shares) will have been duly and validly authorized and issued and will be fully paid and non-assessable.

     (j) All of the issued shares of capital stock of each Significant Subsidiary of the Company have been duly and validly authorized and issued, are fully paid and non-assessable and are owned directly or indirectly by the Company, free and clear of all liens, encumbrances, equities or claims, except as

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described in the Prospectus and except to the extent that any failure of such shares to be free and clear of all liens, encumbrances, equities or claims would not, individually or in the aggregate, have a Material Adverse Effect.

     (k) The Shares are duly authorized for listing on the New York Stock Exchange, subject to notice of issuance.

     (l) The execution and delivery by the Company of, and the performance by the Company of its obligations under, this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument to which the Company or any of its subsidiaries is a party or by which the Company or any of its subsidiaries is bound or to which any of the properties or assets of the Company or any of its subsidiaries is subject, nor will such action result in any violation of the provisions of the Certificate of Incorporation or Bylaws of the Company or any statute or any order, rule or regulation of any court or governmental agency or body having jurisdiction over the Company or any of its subsidiaries or any of their properties, except, in each case other than with respect to such Certificate of Incorporation or Bylaws, for any such conflict, breach, violation or default which would not, individually or in the aggregate, have a Material Adverse Effect and would not impair the Company’s ability to perform its obligations hereunder or have any material adverse effect upon the consummation of the transactions contemplated hereby; and no consent, approval, authorization, order, registration or qualification of or with any such court or governmental agency or body is required for the performance by the Company of its obligations under this Agreement, except for such consents, approvals, authorizations, registrations or qualifications as (i) have been, or will have been prior to the Closing Date, obtained under the Securities Act or the Securities Exchange Act of 1934, as amended (the “Exchange Act”) or (ii) may be required under state securities or Blue Sky laws in connection with the purchase and distribution of the Shares by the Underwriters.

     (m) Neither the Company nor any of its Significant Subsidiaries is in violation of its Certificate of Incorporation or Bylaws or other constituent documents, as applicable, or in default in the performance or observance of any material obligation, covenant or condition contained in any indenture, mortgage, deed of trust, loan agreement, lease or other agreement or instrument to which it is a party or by which it or any of its properties may be bound, except for any such violation or default which would not, individually or in the aggregate, have a Material Adverse Effect.

     (n) Other than as set forth in the Prospectus, there are no legal or governmental proceedings pending to which the Company or any of its subsidiaries is a party or of which any property of the Company or any of its

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subsidiaries is the subject which, if determined adversely to the Company or any of its subsidiaries, would, individually or in the aggregate, have a Material Adverse Effect; and, to the best of the Company’s knowledge, no such proceedings are threatened or contemplated by governmental authorities or threatened by others.

     (o) The Company is not, and after giving effect to the offering and sale of the Shares, will not be, an “investment company”, as such term is defined in the Investment Company Act of 1940, as amended (the “Investment Company Act”).

     (p) Except as set forth in the Prospectus, the Company and its Significant Subsidiaries (i) are in compliance with any and all applicable foreign, federal, state and local laws and regulations relating to the protection of human health and safety, the environment or hazardous or toxic substances or wastes, pollutants or contaminants (“Environmental Laws”), (ii) have received all permits, licenses or other approvals required of them under applicable Environmental Laws to conduct their respective businesses and (iii) are in compliance with all terms and conditions of any such permit, license or approval, except where such noncompliance with Environmental Laws, failure to receive required permits, licenses or other approvals or failure to comply with the terms and conditions of such permits, licenses or approvals would not, singly or in the aggregate, have a Material Adverse Effect.

     (q) Except as set forth in the Prospectus, there are no costs or liabilities associated with Environmental Laws (including, without limitation, any capital or operating expenditures required for clean-up, closure of properties or compliance with Environmental Laws or any permit, license or approval, any related constraints on operating activities and any potential liabilities to third parties) which would, singly or in the aggregate, have a Material Adverse Effect.

     (r) Except as described in the Prospectus, there are no contracts, agreements or understandings between the Company and any person granting such person the right to require the Company to file a registration statement under the Securities Act with respect to any securities of the Company or to require the Company to include such securities with the Shares registered pursuant to the Registration Statement.

     (s) The Company and its Significant Subsidiaries have good and marketable title to all real property and good and marketable title to all personal property owned by them which is material to the business of the Company and its subsidiaries, taken as a whole, in each case free and clear of all liens, encumbrances and defects except such as are described in the Prospectus or such as do not materially affect the value of such property and would not, individually or in the aggregate, have a Material Adverse Effect; and any real property and

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buildings held under lease by the Company or its Significant Subsidiaries are held by them under valid, subsisting and enforceable leases with such exceptions as do not interfere with the use made and proposed to be made of such property and buildings by the Company or its subsidiaries, in each case except as described in the Prospectus and except as would not, individually or in the aggregate, have a Material Adverse Effect.

     (t) The Company and its subsidiaries own or possess, or can acquire on reasonable terms, all material patents, patent rights, licenses, inventions, copyrights, know-how (including trade secrets and other unpatented and/or unpatentable proprietary or confidential information, systems or procedures), trademarks, service marks and trade names currently employed by them in connection with the business now operated by them, and neither the Company nor any of its subsidiaries has received any notice of infringement of or conflict with asserted rights of others with respect to any of the foregoing which, singly or in the aggregate, if the subject of an unfavorable decision, ruling or finding, would have a Material Adverse Affect.

     (u) No labor dispute with the employees of the Company or any of its subsidiaries exists, except as described in the Prospectus, or, to the knowledge of the Company, is imminent, except such as would not have a Material Adverse Effect; and the Company is not aware of any existing, threatened or imminent labor disturbance by the employees of any of its principal suppliers, manufacturers or contractors that could have a Material Adverse Effect on the Company and its subsidiaries, taken as a whole.

     (v) The Company and its subsidiaries are insured by insurers of recognized financial responsibility against such losses and risks and in such amounts as are prudent in the businesses in which they are engaged (such businesses are as described in the Prospectus); and the Company has no reason to believe that the Company will not be able to renew its existing insurance coverage as and when such coverage expires or to obtain similar coverage from similar insurers as may be necessary to continue its businesses at a cost that would not have a Material Adverse Effect on the Company and its subsidiaries, taken as a whole, except as described in the Prospectus.

     (w) The Company and its subsidiaries possess all material certificates, authorizations and permits issued by the appropriate federal, state or foreign regulatory authorities necessary to conduct their respective businesses, and neither the Company nor any of its subsidiaries has received any notice of proceedings relating to the revocation or modification of any such certificate, authorization or permit which, singly or in the aggregate, if the subject of an unfavorable decision, ruling or finding, would have a Material Adverse Effect, except as described in the Prospectus.

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     (x) The Company and each of its subsidiaries maintain a system of internal accounting controls sufficient to provide reasonable assurance that (i) transactions are executed in accordance with management’s general or specific authorizations, (ii) transactions are recorded as necessary to permit preparation of financial statements in conformity with generally accepted accounting principles and to maintain asset accountability, (iii) access to assets is permitted only in accordance with management’s general or specific authorization and (iv) the recorded accountability for assets is compared with the existing assets at reasonable intervals and appropriate action is taken with respect to any differences.

     (y) Except as described in the Prospectus, subsequent to the respective dates as of which information is given in the Registration Statement and the Prospectus, (i) the Company and its subsidiaries have not incurred any liability or obligation, direct or contingent, nor entered into any transaction not in the ordinary course of business, except such as would not have a Material Adverse Effect; (ii) the Company has not purchased any of its outstanding capital stock, nor declared, paid or otherwise made any dividend or distribution of any kind on its capital stock other than ordinary and customary dividends; and (iii) there has not been any material change in the capital stock, short-term debt or long-term debt of the Company and its subsidiaries.

     (z) Prior to the date hereof, neither the Company nor any of its affiliates have taken any action which is designed to or which has constituted or which might have been expected to cause or result in stabilization or manipulation of the price of any security of the Company in connection with the offering of the Shares.

     (aa) Except as described in the Prospectus, the Company has not, as of the date hereof, granted any option, right or warrant to purchase any shares of Common Stock or securities convertible into or exchangeable for Common Stock, in each case that would or could vest within 45 days after the date of the Prospectus, except in the event of a change of control of the Company or termination of employment or death.

     2. Additional Representations and Warranties of the Selling Stockholder. The Selling Stockholder represents and warrants to and agrees with each of the Underwriters that:

     (a) This Agreement has been duly authorized, executed and delivered by the Selling Stockholder and constitutes a valid and binding agreement of the Selling Stockholder.

     (b) The execution and delivery by the Selling Stockholder of, and the performance by the Selling Stockholder of its obligations under, this Agreement, will not conflict with or result in a breach or violation of any of the terms or

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provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument to which the Selling Stockholder or any of its subsidiaries is a party or by which the Selling Stockholder or any of its subsidiaries is bound or to which any of the properties or assets of the Selling Stockholder or any of its subsidiaries is subject, nor will such action result in any violation of the provisions of the Memorandum and Articles of Association of the Selling Stockholder or any statute or any order, rule or regulation of any court or governmental agency or body having jurisdiction over the Selling Stockholder or any of its subsidiaries or any of their properties, except, in each case other than with respect to such Memorandum and Articles of Association, for any such conflict, breach, violation or default which would not, individually or in the aggregate, impair the Selling Stockholder’s ability to perform its obligations hereunder or have any material adverse effect upon the consummation of the transactions contemplated hereby; and no consent, approval, authorization, order, registration or qualification of or with any such court or governmental agency or body is required for the performance by the Selling Stockholder of its obligations under this Agreement, except for such consents, approvals, authorizations, registrations or qualifications as (i) have been, or will have been prior to the Closing, obtained under the Securities Act or the Exchange Act or (ii) may be required under state securities or Blue Sky laws in connection with the purchase and distribution of the Shares by the Underwriters.

     (c) Assuming the Underwriters purchase the Shares to be sold by the Selling Stockholder in good faith and without “notice of an adverse claim” (as such phrase is used in Section 8-105 of the Uniform Commercial Code of the State of Texas (the “Texas UCC”)), upon (i) delivery to the Underwriters of the certificates representing such Shares endorsed in blank by an effective endorsement and (ii) payment therefor in accordance with the terms of this Agreement, the Underwriters will become “protected purchasers” (as defined in Section 8-303(a) of the Texas UCC) of such Shares, free and clear of “adverse claims” (as defined in Section 8-102 of the Texas UCC), except for any such adverse claims created by or at the request of the Underwriters.

     (d) Except as described in the Prospectus, the Selling Stockholder has not granted any option, right or warrant to purchase any shares of Common Stock or securities convertible into or exchangeable for Common Stock, in each case that would or could vest within 45 days after the date of the Prospectus, except in the event of a change of control of the Company or termination of employment or death.

     3. Agreements to Sell and Purchase. The Selling Stockholder hereby agrees to sell to the several Underwriters, and each Underwriter, upon the basis of the representations and warranties herein contained, but subject to the conditions hereinafter stated, agrees, severally and not jointly, to purchase from the Selling Stockholder at $20.1925 a share (the “Purchase Price”), the number of Firm Shares (subject to such

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adjustments to eliminate fractional shares as you may determine) set forth opposite such Underwriter’s name in Schedule I hereto.

     On the basis of the representations and warranties contained in this Agreement, and subject to its terms and conditions, the Selling Stockholder agrees to sell to the Underwriters the Additional Shares, and the Underwriters shall have the right to purchase, severally and not jointly, up to 1,310,000 Additional Shares at the Purchase Price. You may exercise this right on behalf of the Underwriters in whole or from time to time in part by giving written notice of each election to exercise the option not later than 30 days after the date of this Agreement. Any exercise notice shall specify the number of Additional Shares to be purchased by the Underwriters and the date on which such shares are to be purchased. Each purchase date must be at least one business day after the written notice is given and may not be earlier than the closing date for the Firm Shares nor later than ten business days after the date of such notice. Additional Shares may be purchased as provided in Section 5 hereof solely for the purpose of covering over-allotments made in connection with the offering of the Firm Shares. On each day, if any, that Additional Shares are to be purchased (an “Option Closing Date”), each Underwriter agrees, severally and not jointly, to purchase the number of Additional Shares (subject to such adjustments to eliminate fractional shares as you may determine) that bears the same proportion to the total number of Additional Shares to be purchased on such Option Closing Date as the number of Firm Shares set forth in Schedule I hereto opposite the name of such Underwriter bears to the total number of Firm Shares.

     Each of the Company and the Selling Stockholder hereby agrees that, without the prior written consent of Citigroup Global Markets Inc. on behalf of the Underwriters, it will not, during the period ending 45 days after the date of the Prospectus, (i) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any shares of Common Stock or any securities convertible into or exercisable or exchangeable for Common Stock; or (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of the Common Stock, whether any such transaction described in clause (i) or (ii) above is to be settled by delivery of Common Stock or such other securities, in cash or otherwise.

     The restrictions contained in the preceding paragraph shall not apply to (i) the Shares, (ii) the issuance by the Company of shares of Common Stock upon the exercise of an option or warrant or the conversion of a security outstanding on the date hereof, (iii) transactions by any person other than the Company relating to shares of Common Stock or other securities acquired in open market transactions after the completion of the offering of the Shares, (iv) any distribution of shares of Common Stock by the Selling Stockholder to the holders of its ordinary shares by means of a distribution or exchange offer, (v) grants of Common Stock or other securities pursuant to employee benefit plans in existence as of the date hereof or (vi) private sales by the Selling Stockholder of Common Stock or other securities in which the purchaser agrees to be bound by the

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restrictions contained in the preceding paragraph. In addition, the Company agrees that, without the prior written consent of Citigroup Global Markets Inc. on behalf of the Underwriters, it will not, during the period ending 45 days after the date of the Prospectus, file any registration statement with respect to any shares of Common Stock or any security convertible into or exercisable or exchangeable for Common Stock other than the filing by the Company of a registration statement on Form S-8 covering securities issued pursuant to the Company’s 2005 Long Term Incentive Plan.

     4. Terms of Public Offering. The Company and the Selling Stockholder are advised by you that the Underwriters propose to make a public offering of their respective portions of the Shares as soon after the Registration Statement and this Agreement have become effective as in your judgment is advisable. The Company and the Selling Stockholder are further advised by you that the Shares are to be offered to the public initially at $20.50 a share (the “Public Offering Price”) and to certain dealers selected by you at a price that represents a concession not in excess of $0.1850 a share under the Public Offering Price.

     5. Payment and Delivery. Payment for the Firm Shares to be sold by the Selling Stockholder shall be made to the Selling Stockholder in Federal or other funds immediately available in Houston, Texas against delivery of such Firm Shares for the respective accounts of the several Underwriters at 10:00 a.m., Houston time, on May 18, 2005. The time and date of such payment are hereinafter referred to as the “Closing Date.”

     Payment for any Additional Shares shall be made to the Selling Stockholder in Federal or other funds immediately available in Houston, Texas against delivery of such Additional Shares for the respective accounts of the several Underwriters at 10:00 a.m., Houston time, on the date specified in the corresponding notice described in Section 3 hereof or at such other time on the same or on such other date, in any event not later than June 13, 2005, as shall be designated in writing by you.

     The Firm Shares and Additional Shares shall be registered in such names and in such denominations as you shall request in writing not later than one full business day prior to the Closing Date or the applicable Option Closing Date, as the case may be. The Firm Shares and Additional Shares shall be delivered to you on the Closing Date or an Option Closing Date, as the case may be, for the respective accounts of the several Underwriters, with any transfer taxes payable in connection with the transfer of the Shares to the Underwriters duly paid, against payment of the Purchase Price therefor.

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     6. Conditions to the Underwriters’ Obligations. The obligation of the Selling Stockholder to sell the Shares to the Underwriters and the several obligations of the Underwriters to purchase and pay for the Shares on the Closing Date or an Option Closing Date, as applicable, are subject to the condition that the Registration Statement shall have become effective not later than 3:00 p.m. (Houston time) on the date hereof and to the following further conditions:

     (a) Subsequent to the execution and delivery of this Agreement and prior to the Closing Date:

     (i) there shall not have occurred any downgrading, nor shall any notice have been given of any intended or potential downgrading or of any review for a possible change that does not indicate the direction of the possible change, in the rating accorded any of the Company’s securities by any “nationally recognized statistical rating organization,” as such term is defined for purposes of Rule 436(g)(2) under the Securities Act; and

     (ii) there shall not have occurred any change, or any development involving a prospective change, in the general affairs, management, financial position, stockholders’ equity or results of operations, or in the earnings, business or operations of the Company and its subsidiaries, taken as a whole, from that set forth in the Prospectus (exclusive of any amendments or supplements thereto subsequent to the date of this Agreement) that, in the reasonable judgment of Citigroup Global Markets Inc., is material and adverse and that makes it, in the reasonable judgment of Citigroup Global Markets Inc., impracticable to market the Shares on the terms and in the manner contemplated in the Prospectus.

     (b) The Underwriters shall have received on the Closing Date an opinion of Walkers, Cayman Islands counsel for the Selling Stockholder, dated the Closing Date, to the effect that:

     (i) the Selling Stockholder has been duly incorporated and is validly existing as a company in good standing under the laws of the Cayman Islands, with full corporate power and authority to own its properties and conduct its business as described in the Prospectus;

     (ii) This Agreement has been duly authorized and executed and, when delivered by the Selling Stockholder, will constitute the legal, valid and binding obligations of the Selling Stockholder enforceable in accordance with its terms;

     (iii) the execution, delivery and performance of this Agreement and the consummation of the transactions contemplated hereby and the compliance by the Selling Stockholder with the terms and provisions

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hereof do not contravene any law or regulation of the Cayman Islands applicable to the Selling Stockholder or contravene the Memorandum and Articles of Association of the Selling Stockholder; and

     (iv) neither the execution, delivery or performance of this Agreement nor the consummation of any of the transactions contemplated hereby or the compliance by the Selling Stockholder with the terms and provisions hereof, requires the consent or approval of, the giving of notice to, or the registration with, or the taking of any other action in respect of any Cayman Islands governmental or judicial authority or agency.

     The opinion of Walkers described in this Section 6(b) shall be rendered to the Underwriters at the request of the Selling Stockholder and shall so state therein.

     (c) The Underwriters shall have received on the Closing Date an opinion of Baker Botts L.L.P., United States counsel for the Selling Stockholder, dated the Closing Date, to the effect that:

     (i) assuming its due authorization by the Selling Stockholder, and further assuming its due execution and delivery by the Selling Stockholder insofar as such matters are governed by Cayman Islands law, this Agreement has been duly executed and delivered by the Selling Stockholder;

     (ii) the execution and delivery by the Selling Stockholder of, and the performance by the Selling Stockholder of its obligations under, this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument that is identified as an exhibit to the Selling Stockholder’s Annual Report on Form 10-K for the year ended December 31, 2004 nor will such action result in any violation of any statute, rule or regulation or any order known to such counsel of any court or governmental agency or body having jurisdiction over the Selling Stockholder or any of its subsidiaries or any of their properties, except for any such conflict, breach, violation or default which would not, individually or in the aggregate, have a Material Adverse Effect and could not reasonably be expected to adversely affect the Selling Stockholder’s ability to perform its obligations under this Agreement (it being understood that for purposes of this opinion, such counsel shall not be required to pass upon compliance with respect to antifraud or similar provisions of any law, rule or regulation); and no consent, approval, authorization, order, registration or qualification of or with any court or governmental agency or body which, to the best of such counsel’s knowledge, has jurisdiction over the Selling Stockholder or

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any of its subsidiaries or any of their properties is required under the laws of the States of New York or Texas for the performance by the Selling Stockholder of its obligations under this Agreement, except for such consents, approvals, authorizations, registrations or qualifications as (A) have been obtained under the Securities Act and the Exchange Act, (B) may be required under state securities or Blue Sky laws in connection with the purchase and distribution of the Shares by the Underwriters or (C) would not, individually or in the aggregate, have a Material Adverse Effect and could not reasonably be expected to adversely affect the Selling Stockholder’s ability to perform its obligations hereunder or have any material adverse effect upon the consummation of the transactions contemplated hereby; and

     (iii) assuming the Underwriters purchase the Shares to be sold by the Selling Stockholder in good faith and without “notice of an adverse claim” (as such phrase is used in Section 8-105 of the Texas UCC), upon (i) delivery to the Underwriters of the certificates representing such Shares endorsed in blank by an effective endorsement and (ii) payment therefor in accordance with the terms of this Agreement, the Underwriters will become “protected purchasers” (as defined in Section 8-303(a) of the Texas UCC) of such Shares, free and clear of “adverse claims” (as defined in Section 8-102 of the Texas UCC), except for any such adverse claims created by or at the request of the Underwriters.

     Such counsel may rely as to matters of Cayman Islands law upon the opinion of Walkers furnished pursuant to Section 6(b) hereof. Such counsel may limit the foregoing opinions in all respects to the laws of the States of New York and Texas and applicable Federal law, in each case as in effect on the date of such opinions.

     The opinion of Baker Botts L.L.P. described in this Section 6(c) shall be rendered to the Underwriters at the request of the Selling Stockholder and shall so state therein.

     (d) The Underwriters shall have received on the Closing Date an opinion of Porter & Hedges, L.L.P., United States counsel for the Company, dated the Closing Date, to the effect that:

     (i) the Company has been duly incorporated and is validly existing as a corporation in good standing under the laws of the State of Delaware, with corporate power and authority to own its properties and conduct its business as described in the Prospectus;

     (ii) the Company has an authorized capitalization as set forth in the Prospectus, and all of the outstanding shares of capital stock of the

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Company (including the Shares) have been duly authorized and validly issued and are fully paid and non-assessable;

     (iii) this Agreement has been duly authorized, executed and delivered by the Company;

     (iv) the execution and delivery by the Company of, and the performance by the Company of its obligations under, this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument that is identified as an exhibit to the Registration Statement, nor will such action result in any violation of any statute, rule or regulation or any order known to such counsel of any court or governmental agency or body having jurisdiction over the Company or any of its subsidiaries or any of their properties, except for any such conflict, breach, violation or default which would not, individually or in the aggregate, have a Material Adverse Effect and could not reasonably be expected to adversely affect the Company’s ability to perform its obligations under this Agreement (it being understood that for purposes of this opinion, such counsel shall not be required to pass upon compliance with respect to antifraud or similar provisions of any law, rule or regulation); and no consent, approval, authorization, order, registration or qualification of or with any court or governmental agency or body which, to the best of such counsel’s knowledge, has jurisdiction over the Company or any of its subsidiaries or any of their properties is required under the laws of the States of Delaware, New York or Texas for the performance by the Company of its obligations under this Agreement, except for such consents, approvals, authorizations, registrations or qualifications as (A) have been obtained under the Securities Act and the Exchange Act, (B) may be required under state securities or Blue Sky laws in connection with the purchase and distribution of the Shares by the Underwriters or (C) would not, individually or in the aggregate, have a Material Adverse Effect and could not reasonably be expected to adversely affect the Company’s ability to perform its obligations hereunder or have any material adverse effect upon the consummation of the transactions contemplated hereby;

     (v) the Company is not, and after giving effect to the offering and sale of the Shares will not be, an “investment company”, as such term is defined in the Investment Company Act;

     (vi) the statements set forth in the Company’s registration statement on Form 8-A filed with the Commission on February 5, 2004 under the caption “Description of Registrant’s Securities to be Registered” incorporated into the Prospectus, insofar as they purport to constitute a

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summary of the terms of the Company’s capital stock and the statements set forth in the Prospectus under the caption “Underwriters”, insofar as they purport to constitute a summary of the provisions of the laws and documents referred to therein, are accurate in all material respects; and

     (vii) the Registration Statement and the Prospectus and any amendments and supplements thereto made by the Company prior to the Closing Date (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon and other financial and accounting data included therein, or omitted therefrom, as to which such counsel need express no opinion), when they became effective or were filed with the Commission, as the case may be, appeared on their face to comply as to form in all material respects with the requirements of the Securities Act and the rules and regulations thereunder.

     In addition, such counsel shall state that such counsel has participated in conferences with officers and other representatives of the Company and the Selling Stockholder, representatives of the independent public accountants for the Company and representatives of and counsel for the Underwriters at which the contents of the Registration Statement and the Prospectus and related matters were discussed and, although such counsel did not independently verify such information and is not passing upon and does not assume any responsibility for the accuracy, completeness or fairness of the statements contained in the Registration Statement or the Prospectus, except for those referred to in the opinion in clause (vi) of this Section 6(d), on the basis of the foregoing (relying as to materiality to a certain extent upon statements of officers and other representatives of the Company and the Selling Stockholder), no facts have come to such counsel’s attention that would lead such counsel to believe that, as of its effective date, the Registration Statement or any further amendment thereto made by the Company prior to the Closing Date (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon and other financial and accounting data included therein, or omitted therefrom, or the exhibits thereto, as to which such counsel need express no opinion) contained or contains an untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein not misleading or that, as of its date or as of the Closing Date, the Prospectus or any amendment or supplement thereto made by the Company prior to the Closing Date (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon and other financial and accounting data included therein, or omitted therefrom, as to which such counsel need express no opinion) contained or contains an untrue statement of a material fact or omitted or omits to state a material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading.

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     Such counsel may limit the foregoing opinions in all respects to the laws of the States of Delaware, New York and Texas and applicable Federal law, in each case as in effect on the date of such opinions.

     The opinion of Porter & Hedges, L.L.P. described in this Section 6(d) shall be rendered to the Underwriters at the request of the Company and shall so state therein.

     (e) The Underwriters shall have received on the Closing Date an opinion of Eric B. Brown, Senior Vice President, General Counsel and Corporate Secretary of the Selling Stockholder, dated the Closing Date, to the effect that:

     (i) to the best of such counsel’s knowledge, neither the Selling Stockholder nor any of its subsidiaries (other than the Company and its subsidiaries) is in default in the performance or observance of any material obligation, covenant or condition contained in any indenture, mortgage, deed of trust, loan agreement, lease or other agreement or instrument to which it is a party or by which it is bound or to which any of its property or assets is subject, except for any such defaults which would not, individually or in the aggregate, have a Material Adverse Effect; and

     (ii) the execution and delivery by the Selling Stockholder of, and the performance by the Selling Stockholder of its obligations under, this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument known to such counsel (after reasonable inquiry) to which the Selling Stockholder or any of its subsidiaries (other than the Company and its subsidiaries) is a party or by which the Selling Stockholder or any of its subsidiaries (other than the Company and its subsidiaries) is subject, except for any such conflict, breach, violation or default which would not, individually or in the aggregate, have a Material Adverse Effect and could not reasonably be expected to adversely affect the Selling Stockholder’s ability to perform its obligations under this Agreement.

     Such counsel may rely as to matters of Cayman Islands law upon the opinion of Walkers furnished pursuant to Section 6(b) hereof. Such counsel may limit the foregoing opinions in all respects to the laws of the State of Texas and applicable Federal law, in each case as in effect on the date of such opinions.

     The opinion of Eric B. Brown described in this Section 6(e) shall be rendered to the Underwriters at the request of the Selling Stockholder and shall so state therein.

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     (f) The Underwriters shall have received on the Closing Date an opinion of Randall A. Stafford, General Counsel of the Company, dated the Closing Date, to the effect that:

     (i) each of the Significant Subsidiaries has been duly organized, is validly existing and in good standing under the laws of its jurisdiction of organization, with corporate power and authority to own its properties and conduct its business as described in the Prospectus; the Company has been duly qualified as a foreign corporation for the transaction of business and is in good standing under the laws of the State of Texas; THE Offshore Drilling Company has been duly qualified as a foreign corporation for the transaction of business and is in good standing under the laws of the States of Texas and Louisiana; Cliffs Drilling Company has been duly qualified as a foreign corporation for the transaction of business and is in good standing under the laws of the State of Texas and the Bolivarian Republic of Venezuela; and TODCO Mexico Inc. has been duly qualified as a foreign corporation for the transaction of business and is in good standing under the laws of the Mexico;

     (ii) to the best of such counsel’s knowledge, neither the Company nor any of its subsidiaries is in default in the performance or observance of any material obligation, covenant or condition contained in any indenture, mortgage, deed of trust, loan agreement, lease or other agreement or instrument to which it is a party or by which it is bound or to which any of its property or assets is subject, except for any such defaults which would not, individually or in the aggregate, have a Material Adverse Effect;

     (iii) to the best of such counsel’s knowledge and other than as set forth in the Prospectus, there are no legal or governmental proceedings pending to which the Company or any of its subsidiaries is a party or of which any property of the Company or any of its subsidiaries is the subject which, if determined adversely to the Company or any of its subsidiaries, would, individually or in the aggregate, have a Material Adverse Effect; and, to the best of such counsel’s knowledge, no such proceedings are threatened or contemplated by governmental authorities or threatened by others;

     (iv) all of the issued shares of capital stock of each Significant Subsidiary of the Company have been duly and validly authorized and issued, are fully paid and non-assessable and, to the best of such counsel’s knowledge, are owned directly by the Company, free and clear of all liens, encumbrances, equities or claims, except for any such liens, encumbrances, equities or claims described in the Prospectus; and

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     (v) the execution and delivery by the Company of, and the performance by the Company of its obligations under, this Agreement will not conflict with or result in a breach or violation of any of the terms or provisions of, or constitute a default under, any indenture, mortgage, deed of trust, loan agreement or other agreement or instrument known to such counsel (after reasonable inquiry), including any identified as exhibits to the Registration Statement, to which the Company or any of its subsidiaries is a party or by which the Company or any of its subsidiaries is subject, except for any such conflict, breach, violation or default which would not, individually or in the aggregate, have a Material Adverse Effect and could not reasonably be expected to adversely affect the Company’s ability to perform its obligations under this Agreement.

     In addition, such counsel shall state that such counsel has participated in conferences with officers and other representatives of the Company and the Selling Stockholder, representatives of the independent public accountants for the Company and representatives of and counsel for the Underwriters at which the contents of the Registration Statement and the Prospectus and related matters were discussed and, although such counsel did not independently verify such information and is not passing upon and does not assume any responsibility for the accuracy, completeness or fairness of the statements contained in the Registration Statement or the Prospectus, on the basis of the foregoing (relying as to materiality to a certain extent upon statements of officers and other representatives of the Company and the Selling Stockholder), no facts have come to such counsel’s attention that would lead such counsel to believe that, as of its effective date, the Registration Statement or any further amendment thereto made by the Company prior to the Closing Date (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon and other financial and accounting data included therein, or omitted therefrom, or the exhibits thereto, as to which such counsel need express no opinion) contained or contains an untrue statement of a material fact or omitted to state a material fact required to be stated therein or necessary to make the statements therein not misleading or that, as of its date or as of the Closing Date, the Prospectus or any amendment or supplement thereto made by the Company prior to the Closing Date (other than the financial statements and schedules, the notes thereto and the auditors’ report thereon and other financial and accounting data included therein, or omitted therefrom, as to which such counsel need express no opinion) contained or contains an untrue statement of a material fact or omitted or omits to state a material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading; and such counsel does not know of any amendment to the Registration Statement required to be filed or any contracts or other documents of a character required to be filed as an exhibit to the Registration Statement or required to be described in the Registration Statement or the Prospectus which are not filed or incorporated by reference or described as required.

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     For purposes of such counsel’s opinion to be rendered pursuant to Section 6(f)(i) hereof with respect to Significant Subsidiaries, as to matters of the laws of jurisdictions other than the State of Texas and applicable Federal law, such counsel may rely upon opinions of foreign counsel furnished with respect to such Significant Subsidiaries. Such counsel may limit the foregoing opinions in all respects to the laws of the State of Texas and applicable Federal law, in each case as in effect on the date of such opinions.

     The opinion of Randall A. Stafford described in this Section 6(f) shall be rendered to the Underwriters at the request of the Company and shall so state therein.

     (g) The Underwriters shall have received on the Closing Date an opinion of Sullivan & Cromwell LLP, counsel for the Underwriters, dated the Closing Date, covering the matters referred to in clauses (i) (but only as to the due incorporation and valid existence of the Company), (ii) and (vi) (but only as to the statements in the Company’s registration statement on Form 8-A filed with the Commission on February 8, 2004 under the caption “Description of Registrant’s Securities to be Registered” incorporated into the Prospectus and the statements in the Prospectus under the caption “Underwriters”) and the third to last paragraph of Section 6(d) hereof.

     (h) The Underwriters shall have received, on each of the date hereof and the Closing Date, a letter dated the date hereof or the Closing Date, as the case may be, in form and substance agreed by you prior to the execution of this Agreement, from Ernst & Young LLP, independent public accountants, containing statements and information of the type ordinarily included in accountants’ “comfort letters” to underwriters with respect to the financial statements and certain financial information contained in the Registration Statement and the Prospectus; provided that the letter delivered on the Closing Date shall use a “cut-off date” not earlier than the date hereof.

     (i) The “lock-up” agreements between the Underwriters and Mr. Jan Rask, Mr. T. Scott O’Keefe and members of the Board of Directors of the Company, each substantially in the form of Exhibit A hereto (other than in the case of Mr. Jan Rask) or Exhibit B hereto (in the case of Mr. Jan Rask), relating to sales and certain other dispositions of shares of Common Stock or certain other securities, delivered to such persons on or before the date hereof, shall be in full force and effect on the Closing Date.

     (j) The Company and Selling Stockholder shall have furnished or caused to be furnished to the Underwriters on the Closing Date certificates of officers of the Company and Selling Stockholder, respectively, satisfactory to the Underwriters as to the accuracy of the representations and warranties of the Company and Selling Stockholder, respectively, herein at and as of such Closing

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Date, as to the performance by the Company and Selling Stockholder, respectively, of all obligations hereunder to be performed at or prior to such Closing Date, as to the matters set forth in subsection (a) of this Section and as to such other matters as the Underwriters may reasonably request.

     The several obligations of the Underwriters to purchase Additional Shares hereunder are subject to the delivery to you on the applicable Option Closing Date of such documents as you may reasonably request with respect to the good standing of the Company, the due authorization and issuance of the Additional Shares to be sold on such Option Closing Date and other matters related to the issuance of such Additional Shares.

     7. Covenants of the Company. In further consideration of the agreements of the Underwriters herein contained, the Company covenants with each Underwriter as follows:

     (a) To furnish to you, without charge, three signed copies of the Registration Statement (including exhibits thereto) and for delivery to each other Underwriter a conformed copy of the Registration Statement (without exhibits thereto) and to furnish to you in New York City, without charge, prior to 5:00 p.m. New York City time on the business day next succeeding the date of this Agreement and during the period mentioned in Section 7(c) hereof, as many copies of the Prospectus and any supplements and amendments thereto or to the Registration Statement as you may reasonably request.

     (b) Before amending or supplementing the Registration Statement or the Prospectus, to furnish to you a copy of each such proposed amendment or supplement and not to file any such proposed amendment or supplement to which you reasonably object, and to file with the Commission within the applicable period specified in Rule 424(b) under the Securities Act any prospectus required to be filed pursuant to such Rule.

     (c) If, during such period after the first date of the public offering of the Shares and prior to the expiration of nine months after the date of the Prospectus, the Prospectus is required by law to be delivered in connection with sales by an Underwriter or dealer, any event shall occur or condition exist as a result of which it is necessary to amend or supplement the Prospectus in order to make the statements therein, in the light of the circumstances when the Prospectus is delivered to a purchaser, not misleading, or if, in the opinion of counsel for the Underwriters, it is necessary to amend or supplement the Prospectus to comply with applicable law, to prepare, file with the Commission and furnish, at its own expense, to the Underwriters and to the dealers (whose names and addresses you will furnish to the Company) to which Shares may have been sold by you on behalf of the Underwriters and to any other dealers upon request, either amendments or supplements to the Prospectus so that the statements in the Prospectus as so amended or supplemented will not, in the light of the

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circumstances when the Prospectus is delivered to a purchaser, be misleading or so that the Prospectus, as amended or supplemented, will comply with law and if at any time on or after the expiration of nine months after the date of the Prospectus, any Underwriter is required to deliver a prospectus in connection with the offering or sale of the Shares, upon the request but at the expense of such Underwriter, to prepare and furnish to such Underwriter as many copies as such Underwriter may request of an amended Prospectus or a supplemented Prospectus complying with Section 10(a)(3) of the Act.

     (d) To endeavor to qualify the Shares for offer and sale under the securities or Blue Sky laws of such jurisdictions as you shall reasonably request; provided that in connection therewith the Company shall not be required to qualify as a foreign corporation or to file a general consent to service of process in any jurisdiction.

     (e) To make generally available to the Company’s security holders and to you as soon as practicable an earning statement covering the twelve-month period ending May 31, 2006 that satisfies the provisions of Section 11(a) of the Securities Act and the rules and regulations of the Commission thereunder (including, at the option of the Company, Rule 158).

     8. Expenses. Whether or not the transactions contemplated in this Agreement are consummated or this Agreement is terminated, the Company agrees to pay or cause to be paid all expenses incident to the performance of its obligations under this Agreement, including: (i) the fees, disbursements and expenses of the Company’s and the Selling Stockholder’s counsel (except as provided in the following sentence) and the Company’s accountants in connection with the registration and delivery of the Shares under the Securities Act and all other fees or expenses in connection with the preparation and filing of the Registration Statement, any preliminary prospectus, the Prospectus and amendments and supplements to any of the foregoing, including all printing costs associated therewith, and the mailing and delivering of copies thereof to the Underwriters and dealers, in the quantities hereinabove specified, (ii) all costs and expenses related to the transfer and delivery of the Shares to the Underwriters, including any transfer or other taxes payable thereon, (iii) the cost of printing or producing any Blue Sky or Legal Investment memorandum in connection with the offer and sale of the Shares under state securities laws and all expenses in connection with the qualification of the Shares for offer and sale under state securities laws as provided in Section 7(d) hereof, including filing fees and the reasonable fees and disbursements of counsel for the Underwriters in connection with such qualification and in connection with the Blue Sky or Legal Investment memorandum, (iv) all filing fees and the reasonable fees and disbursements of counsel to the Underwriters incurred in connection with the review and qualification of the offering of the Shares by the National Association of Securities Dealers, Inc., (v) all costs and expenses incident to listing the Shares on the New York Stock Exchange, (vi) the cost of printing certificates representing the Shares, (vii) the costs and charges of any transfer agent, registrar or depositary, (viii) the costs and expenses of the Company

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relating to investor presentations on any “road show” undertaken in connection with the marketing of the offering of the Shares, including, without limitation, expenses associated with the production of road show slides and graphics, fees and expenses of any consultants engaged in connection with the road show presentations with the prior approval of the Company, travel and lodging expenses of the representatives and officers of the Company and any such consultants, and the cost of any aircraft chartered in connection with the road show, (ix) the document production charges and expenses associated with printing this Agreement and (x) all other costs and expenses incident to the performance of the obligations of the Company hereunder for which provision is not otherwise made in this Section 8. It is understood, however, that, except as provided in this Section 8, Section 9, and the last paragraph of Section 11 hereof, the Underwriters will pay all of their costs and expenses, including fees and disbursements of their counsel, stock transfer taxes payable on resale of any of the Shares by them and any advertising expenses connected with any offers they may make.

     The provisions of this Section 8 shall not supersede or otherwise affect any other written agreement that the Company and the Selling Stockholder may otherwise have for the allocation of such expenses among themselves.

     9. Indemnity and Contribution. (a) The Company agrees to indemnify and hold harmless each Underwriter, each person, if any, who controls any Underwriter within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act, and each affiliate of any Underwriter within the meaning of Rule 405 under the Securities Act, from and against any and all losses, claims, damages and liabilities (including, without limitation, any legal or other expenses reasonably incurred in connection with defending or investigating any such action or claim) caused by any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or any amendment thereof, any preliminary prospectus or the Prospectus (as amended or supplemented if the Company shall have furnished any amendments or supplements thereto), or caused by any omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, except insofar as such losses, claims, damages or liabilities are caused by any such untrue statement or omission or alleged untrue statement or omission based upon information relating to any Underwriter furnished to the Company in writing by such Underwriter through you expressly for use therein; provided, however, that the foregoing indemnity agreement with respect to any preliminary prospectus shall not inure to the benefit of any Underwriter from whom the person asserting any such losses, claims, damages or liabilities purchased Shares, or any person controlling such Underwriter, if a copy of the Prospectus (as then amended or supplemented if the Company has furnished any amendments or supplements thereto) was not sent or given by or on behalf of such Underwriter to such person, if required by law so to have been delivered, at or prior to the written confirmation of the sale of the Shares to such person, and if the Prospectus (as so amended or supplemented) would have cured the defect giving rise to such losses, claims, damages or liabilities, unless such failure is the result of material noncompliance by the Company with Section 7(a) hereof.

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          (b) The Selling Stockholder agrees to indemnify and hold harmless each Underwriter, each person, if any, who controls any Underwriter within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act, and each affiliate of any Underwriter within the meaning of Rule 405 under the Securities Act, from and against any and all losses, claims, damages and liabilities (including, without limitation, any legal or other expenses reasonably incurred in connection with defending or investigating any such action or claim) caused by any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or any amendment thereof, any preliminary prospectus or the Prospectus (as amended or supplemented if the Company shall have furnished any amendments or supplements thereto), or caused by any omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, in each case to the extent but only to the extent such losses, claims, damages or liabilities are caused by any such untrue statement or omission or alleged untrue statement or omission based upon information relating to the Selling Stockholder furnished to the Company in writing by the Selling Stockholder expressly for use therein; provided, however, that the foregoing indemnity agreement with respect to any preliminary prospectus shall not inure to the benefit of any Underwriter from whom the person asserting any such losses, claims, damages or liabilities purchased Shares, or any person controlling such Underwriter, if a copy of the Prospectus (as then amended or supplemented if the Company has furnished any amendments or supplements thereto) was not sent or given by or on behalf of such Underwriter to such person, if required by law so to have been delivered, at or prior to the written confirmation of the sale of the Shares to such person, and if the Prospectus (as so amended or supplemented) would have cured the defect giving rise to such losses, claims, damages or liabilities; provided, further, that the liability of the Selling Stockholder pursuant to this subsection (b) shall not exceed the product of the number of Shares sold by the Selling Stockholder, including any Additional Shares, and the public offering price per share of the Shares as set forth in the Prospectus.

          (c) Each Underwriter agrees, severally and not jointly, to indemnify and hold harmless the Company, the Selling Stockholder, the directors of the Company, the officers of the Company who sign the Registration Statement and each person, if any, who controls the Company or the Selling Stockholder within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act from and against any and all losses, claims, damages and liabilities (including, without limitation, any legal or other expenses reasonably incurred in connection with defending or investigating any such action or claim) caused by any untrue statement or alleged untrue statement of a material fact contained in the Registration Statement or any amendment thereof, any preliminary prospectus or the Prospectus (as amended or supplemented if the Company shall have furnished any amendments or supplements thereto), or caused by any omission or alleged omission to state therein a material fact required to be stated therein or necessary to make the statements therein not misleading, but only with reference to information relating to such Underwriter furnished to the Company in writing by such Underwriter through you expressly for use in the Registration Statement, any preliminary prospectus, the Prospectus or any amendments or supplements thereto.

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          (d) In case any proceeding (including any governmental investigation) shall be instituted involving any person in respect of which indemnity may be sought pursuant to Section 9(a), 9(b) or 9(c) hereof, such person (the “indemnified party”) shall promptly notify the person against whom such indemnity may be sought (the “indemnifying party”) in writing (but the omission so to notify the indemnifying party shall not relieve it from any liability which it may have to any indemnified party otherwise than under such subsection, except to the extent that indemnifying party suffers actual prejudice as a result of such failure) and the indemnifying party, upon request of the indemnified party, shall retain counsel reasonably satisfactory to the indemnified party to represent the indemnified party and any others the indemnifying party may designate in such proceeding and shall pay the fees and disbursements of such counsel related to such proceeding. In any such proceeding, any indemnified party shall have the right to retain its own counsel, but the fees and expenses of such counsel shall be at the expense of such indemnified party unless (i) the indemnifying party and the indemnified party shall have mutually agreed to the retention of such counsel or (ii) the named parties to any such proceeding (including any impleaded parties) include both the indemnifying party and the indemnified party and representation of both parties by the same counsel would be inappropriate due to actual or potential differing interests between them. It is understood that the indemnifying party shall not, in respect of the legal expenses of any indemnified party in connection with any proceeding or related proceedings in the same jurisdiction, be liable for (i) the fees and expenses of more than one separate firm (in addition to any local counsel) for all Underwriters and all persons, if any, who control any Underwriter within the meaning of either Section 15 of the Securities Act or Section 20 of the Exchange Act or who are affiliates of any Underwriter within the meaning of Rule 405 under the Securities Act and (ii) the fees and expenses of more than one separate firm (in addition to any local counsel) for the Company, the Selling Stockholder, the directors of the Company, the officers of the Company who sign the Registration Statement and each person, if any, who controls the Company or the Selling Stockholder within the meaning of either such Section. In the case of any such separate firm for the Underwriters and such control persons and affiliates of any Underwriters, such firm shall be designated in writing by Citigroup Global Markets Inc. In the case of any such separate firm for the Company, and such directors, officers and control persons of the Company or the Selling Stockholder, such firm shall be designated in writing by the Company and the Selling Stockholder. The indemnifying party shall not be liable for any settlement of any proceeding effected without its written consent, but if settled with such consent or if there be a final judgment for the plaintiff, the indemnifying party agrees to indemnify the indemnified party from and against any loss or liability by reason of such settlement or judgment. No indemnifying party shall, without the prior written consent of the indemnified party, effect any settlement of any pending or threatened proceeding in respect of which any indemnified party is or could have been a party and indemnity could have been sought hereunder by such indemnified party, unless such settlement includes an unconditional release of such indemnified party from all liability on claims that are the subject matter of such proceeding.

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          (e) To the extent the indemnification provided for in Section 9(a), 9(b) or 9(c) hereof is unavailable to an indemnified party or insufficient in respect of any losses, claims, damages or liabilities referred to therein, except to the extent (but only to the extent) that the indemnifying party suffers actual prejudice as a result of any failure by the indemnified party to notify the indemnifying party of any action, proceeding or investigation as contemplated by subsection (d) of this Section 9, each indemnifying party under such paragraph, in lieu of indemnifying such indemnified party thereunder, shall contribute to the amount paid or payable by such indemnified party as a result of such losses, claims, damages or liabilities (i) in such proportion as is appropriate to reflect the relative benefits received by the indemnifying party or parties on the one hand and the indemnified party or parties on the other hand from the offering of the Shares or (ii) if the allocation provided by Section 9(e)(i) hereof is not permitted by applicable law, or if the indemnified party failed to give the notice required under subsection (d) above, then, except to the extent (but only to the extent) that the indemnifying party suffers actual prejudice as a result of any failure by the indemnified party to notify the indemnifying party of any action, proceeding or investigation as contemplated by subsection (d) of this Section 9, in such proportion as is appropriate to reflect not only the relative benefits referred to in Section 9(e)(i) hereof but also the relative fault of the indemnifying party or parties on the one hand and of the indemnified party or parties on the other hand in connection with the statements or omissions that resulted in such losses, claims, damages or liabilities, as well as any other relevant equitable considerations. The relative benefits received by the Company or the Selling Stockholder on the one hand and the Underwriters on the other hand in connection with the offering of the Shares shall be deemed to be in the same respective proportions as the net proceeds from the offering of the Shares (before deducting expenses) received by the Selling Stockholder and the total underwriting discounts and commissions received by the Underwriters, in each case as set forth in the table on the cover of the Prospectus, bear to the aggregate Public Offering Price of the Shares. The relative fault of the Company or the Selling Stockholder on the one hand and the Underwriters on the other hand shall be determined by reference to, among other things, whether the untrue or alleged untrue statement of a material fact or the omission or alleged omission to state a material fact relates to information supplied by the Company or the Selling Stockholder or by the Underwriters and the parties’ relative intent, knowledge, access to information and opportunity to correct or prevent such statement or omission. The Underwriters’ respective obligations to contribute pursuant to this Section 9 are several in proportion to the respective number of Shares they have purchased hereunder, and not joint.

          (f) The Company, the Selling Stockholder and the Underwriters agree that it would not be just or equitable if contribution pursuant to this Section 9 were determined by pro rata allocation (even if the Underwriters were treated as one entity for such purpose) or by any other method of allocation that does not take account of the equitable considerations referred to in Section 9(e) hereof. The amount paid or payable by an indemnified party as a result of the losses, claims, damages and liabilities referred to in the immediately preceding paragraph shall be deemed to include, subject to the limitations set forth above, any legal or other expenses reasonably incurred by such

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indemnified party in connection with investigating or defending any such action or claim. Notwithstanding the provisions of this Section 9, no Underwriter shall be required to contribute any amount in excess of the amount by which the total price at which the Shares underwritten by it and distributed to the public were offered to the public exceeds the amount of any damages that such Underwriter has otherwise been required to pay by reason of such untrue or alleged untrue statement or omission or alleged omission. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution from any person who was not guilty of such fraudulent misrepresentation. The remedies provided for in this Section 9 are not exclusive and shall not limit any rights or remedies which may otherwise be available to any indemnified party at law or in equity.

          (g) The indemnity and contribution provisions contained in this Section 9 and the representations, warranties and other statements of the Company and the Selling Stockholder contained in this Agreement shall remain operative and in full force and effect regardless of (i) any termination of this Agreement, (ii) any investigation made by or on behalf of any Underwriter, any person controlling any Underwriter or any affiliate of any Underwriter, the Selling Stockholder or any person controlling the Selling Stockholder, or the Company, its officers or directors or any person controlling the Company and (iii) acceptance of and payment for any of the Shares; provided, however, that if this Agreement shall be terminated pursuant to Section 10(i), (iii), (iv), or (v) or the second paragraph of Section 11 hereof, the Company and the Selling Stockholder shall have no liability to you other than as set forth in Section 11 hereof.

     10. Termination. The Underwriters may terminate this Agreement by notice given by Citigroup Global Markets Inc. to the Company and the Selling Stockholder, if after the execution and delivery of this Agreement and prior to the Closing Date (i) trading generally shall have been suspended or materially limited on, or by, as the case may be, the New York Stock Exchange or the Nasdaq National Market, (ii) trading of any securities of the Company shall have been suspended on the New York Stock Exchange, (iii) a material disruption in securities settlement, payment or clearance services in the United States shall have occurred, (iv) any moratorium on commercial banking activities shall have been declared by Federal or New York State authorities or (v) there shall have occurred any outbreak or escalation of hostilities, or any adverse change in financial markets or any calamity or crisis that, in the reasonable judgment of Citigroup Global Markets Inc., is material and adverse and which, singly or together with any other event specified in this clause (v), makes it, in the reasonable judgment of Citigroup Global Markets Inc., impracticable or inadvisable to proceed with the offer, sale or delivery of the Shares on the terms and in the manner contemplated in the Prospectus.

     11. Effectiveness; Defaulting Underwriters. This Agreement shall become effective upon the execution and delivery hereof by the parties hereto.

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     If, on the Closing Date or an Option Closing Date, as the case may be, any one or more of the Underwriters shall fail or refuse to purchase Shares that it has or they have agreed to purchase hereunder on such date, and the aggregate number of Shares which such defaulting Underwriter or Underwriters agreed but failed or refused to purchase is not more than one-tenth of the aggregate number of the Shares to be purchased on such date, the other Underwriters shall be obligated severally in the proportions that the number of Firm Shares set forth opposite their respective names in Schedule I bears to the aggregate number of Firm Shares set forth opposite the names of all such non-defaulting Underwriters, or in such other proportions as you may specify, to purchase the Shares which such defaulting Underwriter or Underwriters agreed but failed or refused to purchase on such date; provided that in no event shall the number of Shares that any Underwriter has agreed to purchase pursuant to this Agreement be increased pursuant to this Section 11 by an amount in excess of one-ninth of such number of Shares without the written consent of such Underwriter. If, on the Closing Date, any Underwriter or Underwriters shall fail or refuse to purchase Firm Shares and the aggregate number of Firm Shares with respect to which such default occurs is more than one-tenth of the aggregate number of Firm Shares to be purchased, and arrangements satisfactory to you, the Company and the Selling Stockholder for the purchase of such Firm Shares are not made within 36 hours after such default, this Agreement shall terminate without liability on the part of any non-defaulting Underwriter, the Company or the Selling Stockholder. In any such case either you, the Company or the Selling Stockholder shall have the right to postpone the Closing Date, but in no event for longer than seven days, in order that the required changes, if any, in the Registration Statement and in the Prospectus or in any other documents or arrangements may be effected. If, on an Option Closing Date, any Underwriter or Underwriters shall fail or refuse to purchase Additional Shares and the aggregate number of Additional Shares with respect to which such default occurs is more than one-tenth of the aggregate number of Additional Shares to be purchased on such Option Closing Date, the non-defaulting Underwriters shall have the option to (i) terminate their obligation hereunder to purchase the Additional Shares to be sold on such Option Closing Date or (ii) purchase not less than the number of Additional Shares that such non-defaulting Underwriters would have been obligated to purchase in the absence of such default. Any action taken under this paragraph shall not relieve any defaulting Underwriter from liability in respect of any default of such Underwriter under this Agreement.

     If this Agreement shall be terminated by the Underwriters, or any of them, because of any failure or refusal on the part of the Company or the Selling Stockholder to comply with the terms or to fulfill any of the conditions of this Agreement, or if for any reason the Company or the Selling Stockholder shall be unable to perform its obligations under this Agreement, the Company will reimburse the Underwriters or such Underwriters as have so terminated this Agreement with respect to themselves for all out-of-pocket expenses (including the fees and disbursements of their counsel) reasonably incurred by such Underwriters in connection with this Agreement or the offering contemplated hereunder, but the Company and the Selling Stockholder shall then be under no further liability to you except as provided in Sections 1, 8 and 9.

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     12. Counterparts. This Agreement may be signed in two or more counterparts, each of which shall be an original, with the same effect as if the signatures thereto and hereto were upon the same instrument.

     13. Applicable Law. This Agreement shall be governed by and construed in accordance with the internal laws of the State of New York.

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     14. Headings. The headings of the sections of this Agreement have been inserted for convenience of reference only and shall not be deemed a part of this Agreement.

Accepted as of the date hereof:

Citigroup Global Markets Inc.

Acting severally on behalf of themselves
     and the several Underwriters named in
     Schedule I hereto.

By: Citigroup Global Markets Inc.

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SCHEDULE I

EXHIBIT A

FORM OF LOCK-UP LETTER

[ ], 2005

Citigroup Global Markets Inc.
J.P. Morgan Securities Inc.
UBS Securities LLC

Dear Sirs and Mesdames:

     The undersigned understands that Citigroup Global Markets Inc. (“Citigroup”) and the several underwriters named in Schedule I to the Underwriting Agreement (as defined below), including Citigroup (the “Underwriters”), propose to enter into an Underwriting Agreement (the “Underwriting Agreement”) with TODCO, a Delaware corporation (the “Company”), and its stockholder, Transocean Inc., a Cayman Islands company, providing for the public offering (the “Public Offering”) by the several Underwriters of 13,310,000 shares (the “Shares”) of the Class A common stock (par value $0.01 per share) of the Company (the “Common Stock”).

     To induce the Underwriters that may participate in the Public Offering to continue their efforts in connection with the Public Offering, the undersigned hereby agrees that, without the prior written consent of Citigroup on behalf of the Underwriters, he will not, during the period commencing on the date hereof and ending 45 days after the date of the final prospectus relating to the Public Offering (the “Prospectus”), (i) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any shares of Common Stock or any securities convertible into or exercisable or exchangeable for Common Stock, or (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of the Common Stock, whether any such transaction described in clause (i) or (ii) above is to be settled by delivery of Common Stock or such other securities, in cash or otherwise. The foregoing sentence shall not apply to (a) transactions relating to shares of Common Stock or other securities acquired in the Public Offering or open market transactions after the completion of the Public Offering, (b) transfers of shares of Common Stock or any security convertible into Common Stock as a bona fide gift or gifts and (c) transfers of Common Stock or any security convertible into

A-1

Common Stock by will or intestacy; provided that in the case of any transfer or distribution pursuant to clause (b), (i) each donee or distributee shall execute and deliver to Citigroup a duplicate form of this Lock-up Letter and (ii) no filing by any party (donor, donee, transferor or transferee) under Section 16(a) of the Securities Exchange Act of 1934, as amended, shall be required or shall be made voluntarily in connection with such transfer or distribution (other than a filing on a Form 5). In addition, the undersigned agrees that, without the prior written consent of Citigroup on behalf of the Underwriters, he will not, during the period commencing on the date hereof and ending 45 days after the date of the Prospectus, make any demand for or exercise any right with respect to, the registration of any shares of Common Stock or any security convertible into or exercisable or exchangeable for Common Stock. The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the undersigned’s share of Common Stock except in compliance with the foregoing restrictions.

     The undersigned understands that the Company and the Underwriters are relying upon this Lock-Up Agreement in proceeding toward consummation of the Public Offering. The undersigned further understands that this Lock-Up Agreement is irrevocable and shall be binding upon the undersigned’s heirs, legal representatives, successors and assigns.

     Whether or not the Public Offering actually occurs depends on a number of factors, including market conditions. Any Public Offering will only be made pursuant to an Underwriting Agreement, the terms of which are subject to negotiation between the Company and the Underwriters.

A-2

EXHIBIT B

FORM OF MR. RASK’S LOCK-UP LETTER

Citigroup Global Markets Inc.
J.P. Morgan Securities Inc.
UBS Securities LLC

Dear Sirs and Mesdames:

     The undersigned understands that Citigroup Global Markets Inc. (“Citigroup”) and the several underwriters named in Schedule I to the Underwriting Agreement (as defined below), including Citigroup (the “Underwriters”), propose to enter into an Underwriting Agreement (the “Underwriting Agreement”) with TODCO, a Delaware corporation (the “Company”), and its stockholder, Transocean Inc., a Cayman Islands company, providing for the public offering (the “Public Offering”) by the several Underwriters of 13,310,000 shares (the “Shares”) of the Class A common stock (par value $0.01 per share) of the Company (the “Common Stock”).

     To induce the Underwriters that may participate in the Public Offering to continue their efforts in connection with the Public Offering, the undersigned hereby agrees that, without the prior written consent of Citigroup on behalf of the Underwriters, he will not, during the period commencing on the date hereof and ending 45 days after the date of the final prospectus relating to the Public Offering (the “Prospectus”), (i) offer, pledge, sell, contract to sell, sell any option or contract to purchase, purchase any option or contract to sell, grant any option, right or warrant to purchase, lend, or otherwise transfer or dispose of, directly or indirectly, any shares of Common Stock or any securities convertible into or exercisable or exchangeable for Common Stock, or (ii) enter into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of ownership of the Common Stock, whether any such transaction described in clause (i) or (ii) above is to be settled by delivery of Common Stock or such other securities, in cash or otherwise. The foregoing sentence shall not apply to (a) transactions relating to shares of Common Stock or other securities acquired in the Public Offering or open market transactions after the completion of the Public Offering, (b) transfers of shares of Common Stock or any security convertible into Common Stock as a bona fide gift or gifts and (c) transfers of Common Stock or any security convertible into Common Stock by will or intestacy; provided that in the case of any transfer or distribution pursuant to clause (b), (i) each donee or distributee shall execute and deliver

B-1

to Citigroup a duplicate form of this Lock-up Letter and (ii) no filing by any party (donor, donee, transferor or transferee) under Section 16(a) of the Securities Exchange Act of 1934, as amended, shall be required or shall be made voluntarily in connection with such transfer or distribution (other than a filing on a Form 5). In addition, the undersigned agrees that, without the prior written consent of Citigroup on behalf of the Underwriters, he will not, during the period commencing on the date hereof and ending 45 days after the date of the Prospectus, make any demand for or exercise any right with respect to, the registration of any shares of Common Stock or any security convertible into or exercisable or exchangeable for Common Stock. The undersigned also agrees and consents to the entry of stop transfer instructions with the Company’s transfer agent and registrar against the transfer of the undersigned’s share of Common Stock except in compliance with the foregoing restrictions.

     The undersigned understands that the Company and the Underwriters are relying upon this Lock-Up Agreement in proceeding toward consummation of the Public Offering. The undersigned further understands that this Lock-Up Agreement is irrevocable and shall be binding upon the undersigned’s heirs, legal representatives, successors and assigns.

     This Lock-Up Agreement shall not apply to nor prohibit sales of TODCO Common Stock made on my behalf by Morgan Stanley & Co. Incorporated (“Morgan Stanley”) pursuant to the Preset Diversification Program, attached hereto as Exhibit 1, entered into between the undersigned and Morgan Stanley on March 16, 2005.

     Whether or not the Public Offering actually occurs depends on a number of factors, including market conditions. Any Public Offering will only be made pursuant to an Underwriting Agreement, the terms of which are subject to negotiation between the Company and the Underwriters.

Dated: May___, 2005

B-2

EXHIBIT 1

Preset Diversification Program