Recapitalization Letter Agreement

Exhibit 10.2

HORIZON OFFSHORE, INC.
2500 CityWest Boulevard, Suite 2200
Houston, Texas 77042

March 31, 2005

The Holders of Subordinated Notes Signatory Hereto

Ladies and Gentlemen:

     Reference is made to the Financing Agreement (the “Financing Agreement”) dated as of March 31, 2005 among Horizon Offshore, Inc. (the “Company”), each of its subsidiaries party thereto, Manchester Securities Corp., as collateral and administrative agent (“Manchester”), and the other lenders specified therein (collectively, the “Senior Lenders”), whereby, subject to satisfaction of all conditions precedent set forth therein, the Senior Lenders propose to extend credit in the form of a $70 million senior secured financing facility (the “New Credit Facility”). By your execution of a counterpart of this letter agreement, you acknowledge receipt of a copy of the Financing Agreement. Capitalized terms used and not otherwise defined herein are used with the meanings ascribed thereto in the Financing Agreement.

     The Company and each holder of Subordinated Notes signatory hereto (the “Investors”), in consideration of the mutual agreements and covenants of the parties hereto and the Company’s agreement to issue to the Investors the Recap Common Stock and the New Preferred Stock (as such terms are defined below), hereby agree as follows:

     1. Upon the consummation of the Recap (as defined in paragraph 3 below), you agree that without the need for any further act or evidence, the Subordinated Notes and the Subordinated Note Debt Documents are and shall be deemed amended effective as of the Recap Closing Date (as defined in paragraph 4 below) to (i) reduce the interest rate to 8% per annum; (ii) extend the maturity date to March 31, 2010; and (iii) delete the provisions of the Subordinated Note Debt Documents and events of default specified in Schedule II attached hereto. You agree to take such action and deliver, or cause to be delivered, such agreements, instruments or other documents as the Company and Manchester may reasonably request in order to reflect the amendments and release contemplated by paragraphs 1 and 2 hereof.

     2. You consent to all transactions contemplated by this letter, the Financing Agreement and the other Loan Documents, and agree that the Obligations to be incurred thereunder shall constitute “Refinancing Indebtedness” as that term is defined and used in the Subordinated Note Debt Documents, and you further consent to the assignment to, or releases in favor of, Manchester, as Collateral Agent for the Senior Lenders of all of your rights to the collateral securing the Subordinated Note Debt you hold and the proceeds of such collateral, and you consent to the execution by Elliott Associates, L.P., as collateral agent for the Holders (as defined in the Subordinated Note Debt Documents), of any assignments or releases of security interests and liens existing for your benefit with respect to such collateral (including authorization to file UCC-3 assignment and/or termination statements) and the return to the Company of any cash or other collateral or proceeds thereof held by Elliott Associates, L.P., as such collateral agent.

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     3. The Company will use its best efforts to consummate a series of recapitalization transactions (collectively, the “Recap”) promptly following the funding of the Loans pursuant to which $84,972,823 in aggregate principal amount of Subordinated Notes, representing the aggregate principal amount thereof as of March 31, 2005, and all accrued and unpaid interest for any period after such date prior to the Recap (such that only $25,000,000 aggregate principal amount of Subordinated Notes would remain outstanding, modified as described above) and all 1,400 shares of the Company’s Series A Redeemable Participating Preferred Stock (“Series A Preferred Stock”) would be exchanged for a portion of a new series of one million shares of a convertible preferred stock of the Company (“New Preferred Stock”) and a portion of 60 million newly issued shares of the Company’s common stock (the “Recap Common Stock”). The conversion rate under the New Preferred Stock will be set such that the total outstanding Recap Common Stock and the New Preferred Stock, on an “as converted” basis, will represent in the aggregate 95% of the Company’s common stock on a fully diluted basis (which calculation excludes out-of-the-money director and employee stock options), pro forma for the Recap and the other transactions described herein. The Recap Common Stock and the New Preferred Stock shall also be deemed issued to you by the Company as an inducement to, and as additional consideration for, your agreements to amend the Subordinated Notes and Subordinated Debt Documents set forth in paragraph 1; your consents set forth in paragraph 2; and, if applicable, your commitment to and/or participation in the New Credit Facility as a Senior Lender.

     4. The New Preferred Stock will be issued immediately prior to the issuance of the Recap Common Stock, and will carry an aggregate liquidation preference equal to the greater of (i) $40,000,000 and (ii) the amount the New Preferred Stock would receive on an “as converted” basis (as if the amendment to the Company’s certificate of incorporation referred to below had been adopted). The New Preferred Stock will not entitle holders to any dividend or voting rights (except as required by the Delaware General Corporation Law (the “DGCL”)), will be mandatorily convertible upon amendment to the Company’s certificate of incorporation to increase the number of authorized shares of common stock to accommodate the conversion and to reduce or eliminate any par value for the common shares as deemed necessary or appropriate by the Company and Manchester in connection therewith (but in no event will such mandatory conversion occur prior to six months and one day after the date of initial issuance). The Certificate of Designation, Preferences and Rights of the New Preferred Stock will be substantially in the form of Exhibit A attached hereto. The New Preferred Stock and the Recap Common Stock will be earned (subject to performance by each Investor at the Recap Closing Date as contemplated herein) at the time of funding of the Loans (the “Equity Earned Date”) (with the New Preferred Stock being deemed earned immediately prior to the earning of the Recap Common Stock), and will be issued as promptly as possible following the Equity Earned Date upon consummation of the Recap in accordance with paragraph 3 (the “Recap Closing Date”) after the Company completes the voluntary de-listing of its common stock from the Nasdaq Stock Market and expiration of the waiting period under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 if a filing thereunder is determined to be required by the Company and any Investor in connection with the Recap. If any such filing is determined to be required and is applicable to you, you agree to prepare and make such filing although the Company will reimburse you for your expenses and any filing fee incurred in connection therewith.

     5. The Company will call a meeting of shareholders to be held not earlier than September 15, 2005 nor later than October 31, 2005, to accomplish the amendments to the

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Company’s certificate of incorporation described above, and an amendment to delete the prohibition of action by stockholder consent in lieu of a meeting. You agree to participate in the Recap on a pro rata basis (based upon the aggregate principal amount of Subordinated Notes you hold relative to the aggregate principal amount of all such notes) and to exercise any voting power you may have to approve the amendments to the Company’s certificate of incorporation described above, and to execute such documentation and take such other action as may reasonably be required in connection therewith.

     6. Certain Investors by their execution hereof have agreed to participate in the New Credit Facility as Senior Lenders, and Schedule I hereto sets forth the Term Loan A Commitment and Term Loan B Commitment of each such Senior Lender and Manchester. Schedule I hereto also sets forth for each Investor the number of shares of Recap Common Stock and New Preferred Stock to be received by it as aggregate consideration for the actions to be taken by such Investor reflected in this Agreement (including the commitment to finance). All such shares shall be earned as of the Equity Earned Date, as provided in paragraph 4, and all such shares of New Preferred Stock will be issued in a single transaction on the Recap Closing Date, and all such shares of Recap Common Stock will be issued in a single transaction immediately thereafter.

     7. At the Recap Closing Date, the Company will execute with Manchester, the Senior Lenders and each of you a registration rights agreement in customary form providing for demand, piggyback and resale shelf registration rights concerning (i) the shares of common stock received or receivable by Manchester, each Senior Lender and each of you as a result of the Recap (including upon conversion of New Preferred Stock) and (ii) the Subordinated Notes which remain outstanding after the Recap Closing Date. Such agreement will, among other things, (x) require the Company to file a resale shelf registration statement within 90 days of the Recap Closing Date, to use its best efforts to secure the effectiveness thereof at the earliest possible date, and to maintain such effectiveness at all times thereafter (subject to customary suspension period provisions), and (y) contain customary indemnification and expense reimbursement provisions for your benefit.

     8. You agree that the letter agreement dated October 28, 2004 (effective November 4, 2004) among the Company and the investors party thereto is superseded by this letter and that upon the occurrence of the Equity Earned Date, such agreement shall be of no further effect, except for paragraph 7 thereof, which shall survive such termination.

     9. The Company represents that at the date hereof there are 32,252,658 shares of common stock outstanding and that except for out-of-the money stock options (which do not contain anti-dilution provisions which would be triggered by the Recap) and the Series A Preferred Stock there are no other equity securities outstanding. You represent that the number of shares of the Company’s common stock specified beneath your signature hereto is a true and correct representation of all of the Company’s common stock of which you are a beneficial owner (within the meaning of Rule 16a-1(a)(1) promulgated under the Securities Exchange Act of 1934) as of the date hereof. You further represent that the aggregate original principal amount of each issuance of the Company’s Subordinated Notes that you hold is specified beneath your signature hereto; that such notes are held by you free of any liens or encumbrances; and that you have full authority to execute this letter agreement and to consummate all of the Proposed

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Transactions (as defined below in paragraph 11) as it pertains to you without the requirement of obtaining the consent or authorization of any other person, entity or governmental authority except for any requirements of the Hart-Scott-Rodino Antitrust Improvements Act of 1976, if applicable to you. You agree that, except for sales of common stock pursuant to the resale shelf registration statement contemplated by paragraph 7 hereof (but in no event earlier than the later of (x) the date which is six months and one day following the Recap Closing Date and (y) the automatic conversion of the New Preferred Stock), you will not sell, transfer, pledge or otherwise dispose of any Subordinated Notes you own or any shares of Recap Common Stock or New Preferred Stock you acquire on the Recap Closing Date (each, a “Transfer”) unless you (i) provide at least 10 business days’ prior written notice of such proposed Transfer to the Company, (ii) secure an agreement in writing from the proposed Transferee to adopt, ratify and agree to be bound by and perform this letter agreement as if it were a signatory hereto and furnish the Company with a fully executed counterpart thereof prior to completing such Transfer, which agreement shall expressly name the Company and the other Investors as third party beneficiaries with the right to enforce the Transferee’s obligations thereunder and hereunder, and (iii) otherwise comply with any applicable requirements governing Transfers of Subordinated Notes set forth in the applicable Subordinated Note Debt Documents under which such notes were issued, and applicable requirements of laws governing the Transfer of unregistered securities. You agree that the certificates evidencing New Preferred Stock and Recap Common Stock to be issued to you will bear a legend setting for the Transfer restrictions, voting obligations and the other agreements set forth herein.

     10. Notwithstanding any term to the contrary contained in this letter agreement, the agreements and covenants of the Investors set forth herein are conditioned upon the occurrence of the Equity Earned Date not later than March 31, 2005.

     11. The Company agrees to, and will cause each of its subsidiaries to, indemnify, defend and hold harmless each Investor, each partner, member, shareholder and affiliate of each Investor and each of its and their respective representatives (each, an “Indemnified Party”) from and against any and all claims, actions, damages, losses, liabilities, costs and expenses (including, without limitation, fees and disbursements of counsel), that may be incurred by, asserted or awarded against or imposed upon any Indemnified Party, in each case arising out of or in connection with or relating to any investigation, litigation or proceeding or the preparation of any defense with respect thereto, arising out of or in connection with or relating to this letter agreement, the Recap, the New Credit Facility or any other transaction or action described herein (collectively, the “Proposed Transactions”), whether or not such investigation, litigation or proceeding is brought by the Company, any of its subsidiaries, shareholders or creditors, an Indemnified Party or any other person, or an Indemnified Party is otherwise a party thereto and whether or not the Proposed Transactions are consummated, except to the extent such claim, action, damage, loss, liability, cost or expense is found in a final non-appealable judgment by a court of competent jurisdiction to have resulted from such Indemnified Party’s gross negligence or willful misconduct. IT IS THE INTENT OF THE PARTIES HERETO THAT EACH INDEMNIFIED PARTY BE INDEMNIFIED FOR ITS ORDINARY, SOLE OR CONTRIBUTORY NEGLIGENCE. The Company further agrees that no Indemnified Party shall have any liability (whether direct or indirect, in contract, tort or otherwise) to the Company or any of its subsidiaries, shareholders or creditors for or in connection with this letter agreement or the Proposed Transactions or other actions contemplated hereby, except to the extent such

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liability is expressly set forth in a definitive agreement to which such Indemnified Party is bound or is found in a final non-appealable judgment by a court of competent jurisdiction to have resulted from such Indemnified Party’s gross negligence or willful misconduct. In no event, however, shall any Indemnified Party be liable on any theory of liability for any special, indirect, consequential or punitive damages. In connection with the foregoing obligation to indemnify, defend and hold harmless the Indemnified Parties, the Company agrees that, in the event of anticipated, threatened or actual litigation, it shall, upon demand of an Indemnified Party who determines that it is or is likely to be a party to such anticipated, threatened or actual litigation, advance a reasonable amount of monies relative to such anticipated, threatened or actual litigation in order to fulfill the obligation to defend such Indemnified Party against any and all losses, claims, damages, expenses and liabilities to which such Indemnified Party may become subject in connection with the transactions described herein or the financing contemplated hereby.

     12. (a) From and after the Recap Closing Date, the Company will and you acknowledge that the Company will (and you will not, directly or indirectly, oppose or object to actions taken by the Company to), indemnify and hold harmless each present director and officer of the Company and its Subsidiaries (the “Indemnified Company Parties”), against any costs or expenses (including attorneys’ fees), judgments, fines, losses, claims, damages, liabilities or amounts paid in settlement (collectively, “Costs”) incurred in connection with any claim, action, suit, proceeding or investigation, whether civil, criminal, administrative or investigative, arising out of or pertaining to any act or omission in their capacity as a director or officer occurring on or prior to the Recap Closing Date (including for acts or omissions in connection with the approval of this letter agreement and the consummation of the transactions contemplated hereby), whether asserted or claimed prior to, at or after the Recap Closing Date, to the fullest extent permitted under applicable law (and the Company shall also advance reasonable expenses as incurred to the fullest extent permitted under applicable law; provided that, if required by applicable law, the Indemnified Company Party to whom expenses are advanced provides an undertaking to repay such advances if it is ultimately determined that such Indemnified Party is not entitled to indemnification). For four years from the Recap Closing Date, the Company will, and you acknowledge that the Company will (and you will not, directly or indirectly, oppose or object to any actions taken by the Company to) maintain in effect for the benefit of the Company’s current directors and officers an insurance and indemnification policy that provides coverage for acts or omissions occurring prior to the Recap Closing Date (the “D&O Insurance”) covering each such person currently covered by the officers’ and directors’ liability insurance policies of the Company on terms with respect to coverage and in amounts no less favorable than those of the Company’s policies in effect on the date hereof with the same or comparable quality insurance carriers; provided, however, that the Company shall not be required to pay an annual premium for the D&O Insurance in excess of 200% of the premium for the 2004 fiscal year (the “Maximum Premium”); provided, further, however, if such D&O Insurance coverage cannot be obtained at all, or can only be obtained at an annual premium in excess of the Maximum Premium, the Company shall obtain the most advantageous policies of directors’ and officers’ insurance obtainable for an annual premium equal to the Maximum Premium. The provisions of this paragraph 12 are intended to be in addition to the rights otherwise available to the current and former officers and directors of the Company by applicable law, charter, by-law or agreement. You acknowledge that the Company will (and you will not, directly or indirectly, oppose or object to actions taken by the Company to) keep in

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effect after the Recap Closing Date provisions in its certificate of incorporation and bylaws providing for exculpation of director and officer liability and its indemnification of the Indemnified Company Parties to the fullest extent permitted under the DGCL, which provisions will not be amended except as required by applicable law or except to make changes permitted by law that would enlarge the Indemnified Company Parties’ right of indemnification. You acknowledge that the Company will (and you will not, directly or indirectly, oppose or object to actions taken by the Company to) honor any of the indemnification agreements entered into with its directors and keep in effect after the Recap Closing Date all of the provisions in its certificate of incorporation and bylaws providing for exculpation of director and officer liability and its indemnification of the Indemnified Company Parties to the fullest extent permitted under the DGCL, which provisions will not be amended except as required by applicable law or except to make changes permitted by law that would enlarge the “Indemnified Company Parties” right of indemnification.

     (b) In the event that the Company or its successors or assigns (i) consolidates with or merges into any other person and is not the continuing or surviving corporation or entity of such consolidation or merger or (ii) transfers or conveys all or substantially all its properties and assets to any person, then, and in each such case, the Company shall, as a condition precedent to any such transaction, cause proper provisions to be made so that the successors and assigns of the Company assume the obligations set forth in this paragraph 12. The obligations of the Company under this paragraph 12 shall not be terminated or modified in such a manner as to adversely affect any indemnitee to whom this paragraph 12 applies without the express written consent of such affected indemnitee (it being expressly agreed that the indemnitees to whom this paragraph 12 applies shall be third party beneficiaries of this paragraph 12).

     13. Except as provided in paragraph 12(b), this letter agreement may not be amended or waived except by an instrument in writing signed by the Company and each Investor. This letter agreement may be executed in any number of counterparts, no one of which need be signed by all parties but each of which shall be an original, and all of which, when taken together, shall constitute one agreement. Delivery of an executed signature page of this letter agreement by facsimile transmission shall be effective as delivery of a manually executed counterpart hereof. This letter agreement will become effective upon execution of a counterpart hereof by each Investor.

     14. Each of the Investors hereby represents and warrants that in making its decision to enter into this letter agreement, to undertake the obligations to performed by it hereunder and to participate in the Recap, it has independently, and without reliance upon Manchester or any of its affiliates, and based on such information as such Investor has deemed appropriate, made its own investment and credit analyses and decision to enter into this letter agreement.

     15. The Company and each Investor hereby irrevocably waives all right to trial by jury in any action, proceeding or counterclaim (whether based on contract, tort or otherwise) arising out of or relating to this letter agreement or the Proposed Transactions or the actions of the Company, any Investor or any of its respective representatives in the negotiation, performance or enforcement hereof.

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     16. You acknowledge and agree that Manchester and its affiliates are intended third party beneficiaries under this letter agreement.

     17. This letter agreement shall be construed in accordance with, and this letter agreement and all matters arising out of or relating in any way whatsoever to it (whether in contract, tort or otherwise) shall be governed by the laws of the State of New York.

[Signature pages to follow]

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     Please confirm that the foregoing is our mutual understanding by signing and returning to the Company an executed counterpart of this letter agreement.

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SCHEDULE I

SCHEDULE II

Each of the Purchase Agreement related to the Company’s 18% Subordinated Secured Notes due March 31, 2007 and the Purchase Agreement related to the Company’s 16% Subordinated Secured Notes due March 31, 2007 (in each case before giving effect to paragraph 1 of the letter agreement to which this Schedule II is attached) is amended, by execution of the letter agreement, without the need for further act or evidence, to delete therefrom:

     Terms of the Notes: Section 2.2(c)

     Covenants: All of Article 6

     Events of Default: All of Section 7.1, except Sections 7.1.1, 7.1.4, 7.1.6 and 7.1.8

provided, however, if required by the holders of a majority of the outstanding Subordinated Notes, in lieu of deletion of certain affirmative covenants, those covenants may be retained and amended or revised as would be appropriate for publicly traded debt securities of an investment grade issuer.

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Exhibit A

HORIZON OFFSHORE, INC.

CERTIFICATE OF DESIGNATION,
PREFERENCES AND RIGHTS
OF
SERIES B MANDATORILY CONVERTIBLE REDEEMABLE

PREFERRED STOCK

Pursuant to Section 151 of the
Delaware General Corporation Law

      HORIZON OFFSHORE, INC. (the “Company”), a corporation organized and existing under the laws of the State of Delaware, hereby certifies that pursuant to the provisions of Section 151 of the Delaware General Corporation Law, its Board of Directors, at a duly noticed and convened meeting held on March 29, 2005 adopted the following resolution, which resolution remains in full force and effect as of the date hereof:

      WHEREAS, the Board of Directors of the Company is authorized, within the limitations and restrictions stated in the Certificate of Incorporation, to fix by resolution or resolutions the designation of preferred stock and the powers, preferences and relative participating, optional or other special rights and qualifications, limitations or restrictions thereof, including, without limiting the generality of the foregoing, such provisions as may be desired concerning voting, redemption, dividends, dissolution or the distribution of assets, conversion or exchange, and such other subjects or matters as may be fixed by resolution or resolutions of the Board of Directors under the Delaware General Corporation Law; and

      WHEREAS, it is the desire of the Board of Directors of the Company, pursuant to its authority as aforesaid, to authorize and fix the terms of the preferred stock to be designated the Series B Mandatorily Convertible Redeemable Preferred Stock of the Company and the number of shares constituting such preferred stock;

      NOW, THEREFORE, BE IT RESOLVED, that there is hereby authorized the Series B Mandatorily Convertible Redeemable Preferred Stock on the terms and with the provisions herein set forth:

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DESIGNATION, PREFERENCES AND RIGHTS

of

SERIES B MANDATORILY CONVERTIBLE REDEEMABLE PREFERRED STOCK

of

HORIZON OFFSHORE, INC.

      The relative rights, preferences, powers, qualifications, limitations and restrictions granted to or imposed upon the Series B Mandatorily Convertible Redeemable Preferred Stock or the holders thereof are as follows:

      1. Definitions. For purposes of this Certificate of Designation, Preferences and Rights of Series B Mandatorily Convertible Redeemable Preferred Stock (this “Certificate of Designation”) the following definitions shall apply:

      “Amendment” shall mean receipt by the Company from the Delaware Secretary of State of confirmation of filing of a Certificate of Amendment of the Company’s Certificate of Incorporation, as amended, that (a) increases the number of authorized shares of Common Stock to one billion shares and (b) reduces the par value for such shares to not more than $.00001 per share duly approved and adopted by the Board and the Company’s stockholders in accordance with Section 242 of the Delaware General Corporation Law and all other applicable laws, rules and regulations.

      “Board” shall mean the Board of Directors of the Company.

      “Common Stock” shall mean the Common Stock, par value $1.00 per share, of the Company, as constituted from time to time; provided however, the Common Stock as constituted from time to time shall have only the voting powers and rights appurtenant to the Common Stock existing at the Original Issue Date.

      “Company” shall mean Horizon Offshore, Inc., a Delaware corporation.

      “Conversion Rate” has the meaning set forth in Section 7(a) of this Certificate of Designation.

      “Current Market Price,” when used with reference to shares of Common Stock or other securities on any date, shall mean the average of the daily market prices for 20 consecutive trading days commencing 30 days before such date. The daily market price for each such trading day shall be the average of the last reported closing bid and asked prices on such day as officially quoted on the NASDAQ National Market, (a) if the Common Stock is not then listed or admitted to trading on any stock exchange or such market, the average of the last reported closing bid and asked prices on such day on the OTC Bulletin Board (or similar system on such day) as furnished by NASDAQ or Pink Sheets, LLC, (b) if neither such entity at the time is engaged in the business of reporting

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such prices, as furnished by any similar firm then engaged in such business, or (c) if there is no such firm, as furnished by any member of the National Association of Securities Dealers (“NASD”) selected mutually by the Required Holders and the Company or, if they cannot agree upon such selection, as selected by two such members of the NASD, one of which shall be selected by the Required Holders and one of which shall be selected by the Company.

      “Fully Diluted Outstanding” shall mean, with reference to Common Stock, at any date as of which the number of shares thereof is to be determined, (a) all shares of Common Stock outstanding at such date and (b) all shares of Common Stock underlying other options or warrants to purchase, or other securities convertible into or exchangeable for, shares of Common Stock outstanding on such date excluding any such options, warrants or securities with an exercise or conversion price in excess of the Current Market Price.

      “Liquidation Preference” shall mean $40.00 per share for each share of the Mandatorily Convertible Preferred Stock.

      “Mandatorily Convertible Preferred Stock” shall refer to shares of Series B Mandatorily Convertible Redeemable Participating Preferred Stock, $1.00 par value per share, of the Company.

      “Original Issue Date” shall mean the date of the original issuance of shares of Mandatorily Convertible Preferred Stock.

      “Person” shall mean any individual, firm, corporation or other entity, and shall include any successor (by merger or otherwise) of such entity.

      “Redemption Date” shall mean March 31, 2011.

      “Redemption Price” shall mean, at any date of determination, a per share amount equal to the Liquidation Preference hereof increased at a rate of 10% per annum, compounded quarterly at the end of each fiscal quarter of the Company (commencing June 30, 2005).

      “Required Holders” shall mean the holders of at least of a majority of the outstanding shares of Mandatorily Convertible Preferred Stock.

      “Six Month Anniversary Date” has the meaning set forth in Section 7(a) of this Certificate of Designation.

      2. Designation; Number of Shares. The designation of the preferred stock authorized by this resolution shall be “Series B Mandatorily Convertible Redeemable Participating Preferred Stock” and the number of shares of Series B Mandatorily Convertible Redeemable Participating Preferred Stock authorized hereby shall be 1,000,000 shares.

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      3. Dividends.

      (a) No dividends shall be declared or paid on shares of Mandatorily Convertible Preferred Stock.

      (b) So long as any shares of Mandatorily Convertible Preferred Stock shall be outstanding, no dividend whatsoever shall be paid or declared, and no distribution shall be made, on account of any Common Stock or of Common Stock (or any security convertible or exchangeable therefor.

      4. Liquidation Rights of Mandatorily Convertible Preferred Stock.

      (a) In the event of any liquidation, dissolution or winding up of the Company, whether voluntary or involuntary, the holders of Mandatorily Convertible Preferred Stock then outstanding shall be entitled to be paid out of the assets of the Company available for distribution to its stockholders, whether such assets are capital, surplus or earnings, before any payment or declaration and setting apart for payment of any amount shall be made in respect of any shares of Common Stock or any share of any other class or series of the Company’s preferred stock ranking junior to the Mandatorily Convertible Preferred Stock with respect to the payment of dividends or distribution of assets on liquidation, dissolution or winding up of the Company, an amount in cash equal to the greater of (i) the Liquidation Preference and (ii) such amount per share as would have been payable had each such share been converted to Common Stock pursuant to Section 7 immediately prior to such liquidation, dissolution or winding up of the Company.

      (b) If upon any liquidation, dissolution or winding up of the Company, whether voluntary or involuntary, the assets to be distributed among the holders of Mandatorily Convertible Preferred Stock shall be insufficient to permit the payment to such stockholders of the full preferential amounts aforesaid, then the entire assets of the Company to be distributed shall be distributed ratably among the holders of Mandatorily Convertible Preferred Stock, based on the full preferential amounts for the number of shares of Mandatorily Convertible Preferred Stock held by each holder.

      (c) After payment to the holders of Mandatorily Convertible Preferred Stock of the amounts set forth in Section 4(a) hereof, the entire remaining assets and funds of the Company legally available for distribution, if any, shall be distributed among the holders of any Company stock entitled to a preference over the Common Stock in accordance with the terms thereof and, thereafter, to the holders of Common Stock.

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      5. Voting Rights. Holders of Mandatorily Convertible Preferred Stock shall have no voting rights, except as provided by law; provided, however that the affirmative vote of the Required Holders, voting together as a class, in person or by proxy, at a special or annual meeting of such holders called for the purpose, or pursuant to a written consent of such holders, shall be necessary to:

      (a) authorize, adopt or approve an amendment or alteration to, or repeal of, the Certificate of Incorporation of the Company (whether pursuant to Section 242 or 251(e) of the Delaware General Corporation Law, merger, consolidation or otherwise) which would alter or change in any manner the terms, powers, preferences or special rights of the shares of the Mandatorily Convertible Preferred Stock or grant waivers thereof, or which would otherwise adversely affect the rights of the Mandatorily Convertible Preferred Stock, provided that no such modification or amendment may, without the consent of each holder of Mandatorily Convertible Preferred Stock affected thereby; (i) change the Conversion Rate; (ii) change the Redemption Date; (iii) reduce the Liquidation Preference or Redemption Price of the Mandatorily Convertible Preferred Stock; or (iv) reduce the percentage of outstanding Mandatorily Convertible Preferred Stock necessary to modify or amend the terms thereof or to grant waivers thereof; or

      (b) issue any shares of the Common Stock, or shares of other capital stock of the Company ranking senior to, or pari passu with, or junior to (either as to dividends or upon voluntary or involuntary liquidation, dissolution or winding up) the Mandatorily Convertible Preferred Stock, or issue any securities, notes, warrants, options or other instruments convertible into, exercisable for or exchangeable for such shares.

      6. Redemption of Mandatorily Convertible Preferred Stock.

      (a) The Company shall redeem, and the holders of the outstanding Mandatorily Convertible Preferred Stock shall sell to the Company on the Redemption Date, for cash at the Redemption Price, all of the outstanding Mandatorily Convertible Preferred Stock.

      (b) On or before the Redemption Date, each holder of Mandatorily Convertible Preferred Stock shall surrender the certificate or certificates representing such shares of Mandatorily Convertible Preferred Stock to the Company, in the manner and at the place designated in the written notice of redemption provided by the Company, and thereupon the Redemption Price for such shares shall be payable in the manner described in Section 6(c) on the Redemption Date to the person whose name appears on such certificate or certificates as the owner thereof, and each surrendered certificate shall be cancelled and retired.

      (c) The Redemption Price shall be payable in cash at the Redemption Date upon any redemption pursuant to Section 6(a).

      (d) Unless the Company shall fail to redeem the shares of Mandatorily Convertible Preferred Stock when the Company is required to do so, the holders of shares

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of Mandatorily Convertible Preferred Stock which are to be redeemed shall cease to have any further rights with respect thereto on the Redemption Date, other than to receive the applicable Redemption Price, which shall be without interest.

      (e) If, at the time of any redemption pursuant to Section 6(a), the funds of the Company legally available for redemption of Mandatorily Convertible Preferred Stock are insufficient to redeem the number of shares required to be redeemed, those funds which are legally available shall be used to redeem the maximum possible number of such shares, pro rata based upon the number of shares to be redeemed. At any time thereafter when additional funds of the Company become legally available for the redemption of Mandatorily Convertible Preferred Stock, such funds shall immediately be used to redeem the balance of the shares of Mandatorily Convertible Preferred Stock which the Company has become obligated to redeem pursuant to this Section 6(e).

      (f) The Company may not otherwise redeem or repurchase the Mandatorily Convertible Preferred Stock.

      7. Conversion.

      (a) Automatic Conversion. Upon the occurrence of the Amendment, all the shares of Mandatorily Convertible Preferred Stock shall automatically convert into fully paid and nonassessable shares of Common Stock at the Conversion Rate; provided, however, if the Amendment occurs prior to the date which is six months and one day from and after the Original Issue Date ( the “Six Month Anniversary Date”), no conversion will occur until the Six Month Anniversary Date . The “Conversion Rate” means, for each share of Mandatorily Convertible Preferred Stock, a number of shares of Common Stock calculated as follows:

Conversion Rate = (X — [60,000,000 plus the number of Fully Diluted Outstanding
Shares of Common Stock on March 31, 2005])/1,000,000;

where X equals the number of Fully Diluted Outstanding shares of Common Stock on March 31, 2005 divided by .05, as such rate may be adjusted from time to time as provided in Section 7(e) below.

      (b) Fractional Shares. No fractional shares of Common Stock will be issued upon conversion of the Mandatorily Convertible Preferred Stock. In lieu of fractional shares, the Company will round up to the nearest whole share the number of shares of Common Stock issued upon conversion of the Mandatorily Convertible Preferred Stock.

      (c) Exchange of Certificates. The conversion of the Mandatorily Convertible Preferred Stock into Common Stock shall be effective immediately upon public announcement by the Company of the automatic conversion provided for in Section 7(a) and each certificate representing shares of Convertible Preferred Stock shall then be deemed thereafter to represent shares of Common Stock without any further

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action on the part of the holders of such shares and whether or not the certificates representing such shares are surrendered to the Company; provided, however, that promptly after such conversion, the Company shall provide notice of such conversion to the holders of the Convertible Preferred Stock and from and after such notice, each holder will be entitled to surrender the certificate or certificates for the shares of Mandatorily Convertible Preferred Stock at the office of the transfer agent (or at the principal office of the Company if the Company serves as its own transfer agent) together with a notice as to whether the certificate or certificates for shares of Common Stock to be issued shall be in such holder’s name or the names of such holder’s nominee(s). If required by the Company, certificates surrendered after conversion will be endorsed or accompanied by a written instrument or instruments of transfer, in form reasonably satisfactory to the Company, duly executed by the holder or his, her or its attorney duly authorized in writing. The Company will, as soon as practicable after the Amendment, issue and deliver at such office to such holder, or to such holder’s nominee(s), a certificate or certificates for the number of shares of Common Stock to which such holder is entitled. Such conversion will be deemed to have been made immediately after the Amendment, and the Person or Persons entitled to receive the shares of Common Stock issuable upon such conversion will be treated for all purposes as the record holder or holders of such shares of Common Stock as of such date.

      (d) Stock Splits, Dividends and Distributions. So long as any shares of Mandatorily Convertible Preferred Stock are outstanding, the Company will not effect any split or subdivision of the outstanding shares of Common Stock.

      (e) Adjustment for Reorganization, Reclassification or Exchange. If the Common Stock issuable upon the conversion of the Mandatorily Convertible Preferred Stock is changed into or exchanged for the same or a different number of shares of any class or classes of stock of the Company or another entity, whether by capital reorganization, merger, consolidation, reclassification, or otherwise then and in each such event the holders will have the right upon conversion to receive such shares of the kind and amount of shares of stock and other securities and property receivable upon such capital reorganization, merger, consolidation, reclassification, or other change such that its conversion rights and the Conversion Rate with respect to Common Stock of the Company or such other entity will be maintained upon the occurrence of the Amendment.

      (f) No Impairment. The Company will not, by amendment of its Certificate of Incorporation or through any reorganization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities or any other voluntary action, modify, amend, abrogate, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed hereunder by the Company, but will at all times in good faith assist in the carrying out of all the provisions of this Certificate of Designation and in the taking of all such action as may be necessary or appropriate to protect the conversion rights and other rights and preferences of the holders of the Mandatorily Convertible Preferred Stock against impairment.

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      (g) Certificate as to Adjustments. The Company will, upon the written request at any time of any holder of Mandatorily Convertible Preferred Stock, furnish or cause to be furnished to such holder a certificate setting forth the number of shares of Common Stock and the amount, if any, of other property which then would be received upon the conversion of Mandatorily Convertible Preferred Stock.

      8. Remedies. Any registered holder of Mandatorily Convertible Preferred Stock may proceed to protect and enforce its rights and the rights of such holders by any available remedy by proceeding at law or in equity to protect and enforce any such rights, whether for the specific enforcement of any provision in this Certificate of Designation or in aid of the exercise of any power granted herein, or to enforce any other proper remedy.

      9. No Reissuance of Mandatorily Convertible Preferred Stock. No Mandatorily Convertible Preferred Stock acquired by the Company by reason of redemption, purchase, or otherwise shall be reissued, and all such shares shall be cancelled, retired and eliminated from the shares which the Company shall be authorized to issue.

      10. Notices. All notices to the Company permitted hereunder shall be personally delivered or sent by first class mail, postage prepaid, addressed to its principal office located at 2500 CityWest Boulevard, Suite 2200, Houston, Texas 77042, or to such other address at which its principal office is located and as to which notice thereof is similarly given to the holders of the Mandatorily Convertible Preferred Stock at their addresses appearing on the books of the Company.

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      11. Legend. Each certificate representing shares of Mandatorily Convertible Preferred Stock shall bear the following legend:

“THE SECURITIES EVIDENCED BY THIS CERTIFICATE HAVE BEEN ACQUIRED FOR INVESTMENT AND THE OFFER AND SALE OF THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR ANY STATE SECURITIES OR BLUE SKY LAWS. THESE SECURITIES MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM UNDER SAID ACT OR APPLICABLE STATE SECURITIES OR BLUE SKY LAWS. ADDITIONALLY, THE TRANSFER OF THESE SECURITIES IS SUBJECT TO THE CONDITIONS SPECIFIED IN A LETTER AGREEMENT DATED AS OF MARCH 31, 2005, AMONG THE ISSUER HEREOF AND CERTAIN OTHER PARTIES THERETO, AND NO TRANSFER OF THESE SECURITIES SHALL BE VALID OR EFFECTIVE UNTIL SUCH CONDITIONS HAVE BEEN FULFILLED. A COPY OF SUCH AGREEMENT MAY BE OBTAINED AT NO COST BY WRITTEN REQUEST MADE BY THE HOLDER OF RECORD OF THIS CERTIFICATE TO THE SECRETARY OF THE ISSUER HEREOF.”

[Remainder of Page Intentionally Left Blank]

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      IN WITNESS WHEREOF, Horizon Offshore, Inc. has caused this Certificate to be signed by its President and Secretary, respectively, on this 31 day of March, 2005.