FIRST AMENDMENT TO RIGHTS AGREEMENT

Exhibit 4.1

FIRST AMENDMENT TO RIGHTS AGREEMENT

     This FIRST AMENDMENT (this “Amendment”) dated as of June 3, 2008, to the Rights Agreement, dated as of May 31, 2002 (the “Rights Agreement”), by and between W-H Energy Services, Inc., a Texas corporation (the “Company”), and Computershare Trust Company, N.A., successor-in-interest to Computershare Trust Company, Inc., as rights agent (the “Rights Agent”).

     WHEREAS, the Company and the Rights Agent are parties to the Rights Agreement; and

     WHEREAS, on June 2, 2008, the Board of Directors of the Company approved the terms of an Agreement and Plan of Merger (the “Merger Agreement”) by and among the Company, Smith International, Inc., a Delaware corporation (“Parent”), and Whitehall Acquisition Corp., a Texas corporation (“Acquisition”), pursuant to which Parent would commence an exchange offer (the “Offer”) to purchase shares of the Company’s common stock, par value $.0001 per share (“Common Stock”), followed by a merger (the “Merger”) in which Acquisition would be merged with and into the Company and the Company, as the surviving corporation (the “Surviving Corporation”), would become a direct, wholly owned subsidiary of Parent, and as soon as practicable following the Merger, Parent would cause the Surviving Corporation to be merged with an into a wholly owned subsidiary of Parent (the “Second Merger,” and together with the Merger, the “Mergers”), with such subsidiary surviving the Second Merger; and

     WHEREAS, the Merger Agreement grants Acquisition an irrevocable option to purchase (the “Top-Up Option”) certain newly-issued shares of Common Stock; and

     WHEREAS, the Board of Directors of the Company has determined that, in connection with the transactions contemplated by the Merger Agreement, including the Offer and the Mergers, an amendment to the Rights Agreement as set forth herein is necessary and desirable;

     WHEREAS, pursuant to Section 27 of the Rights Agreement, the Company may from time to time in its discretion supplement or amend the Rights Agreement pursuant to an amendment duly executed by the Company and the Rights Agent;

     NOW, THEREFORE, pursuant to the terms of the Rights Agreement and in accordance with Section 27 thereof, the following actions are hereby taken prior to executing the Merger Agreement:

     Section 1. Amendments to Rights Agreement. The Rights Agreement is hereby amended as follows:

     (a) The definition of “Acquiring Person” in Section 1 of the Rights Agreement is amended to add the following sentence at the end the paragraph: “Notwithstanding the foregoing, neither Parent, Acquisition nor any of their respective, existing or future Affiliates or Associates shall be, or be deemed to be, an Acquiring Person, either individually or collectively, by virtue of (i) the public or other announcement of the Merger Agreement or any transaction contemplated thereby or arising in connection therewith, including, without limitation, the Offer, the Top-Up Option or the Mergers, (ii) the acquisition of Common Shares (including, without limitation, any

options, warrants or other securities and rights to acquire Common Shares and upon the conversion of shares of common stock of Acquisition into Common Shares of the Company in the Merger) of the Company pursuant to or in connection with the Merger Agreement or any transaction contemplated thereby or arising in connection therewith, including without limitation, the Offer, the Mergers or the Top-Up Option, (iii) the approval, execution or delivery of the Merger Agreement or (iv) the commencement or consummation of the Offer, the Mergers or the Top-Up Option or any other transactions contemplated by or arising in connection with the Merger Agreement or any other agreement, instrument or document contemplated by the Merger Agreement (each of the events described in clauses (i), (ii), (iii) or (iv) and any combination thereof, an “Exempt Event”).”

     (b) The definition of “Beneficial Owner” and “beneficially owned” in Section 1 of the Rights Agreement is amended to delete the last sentence in its entirety and replace it with the following:

“Notwithstanding anything in this definition of Beneficial Ownership to the contrary, (A) the phrase “then outstanding,” when used with reference to a Person’s Beneficial Ownership of securities of the Company, shall mean the number of such securities then issued and outstanding together with the number of such securities not then actually issued and outstanding which such Person would be deemed to own beneficially hereunder and (B) for purposes of this Agreement, neither Parent, Acquisition nor any of their respective Affiliates or Associates shall be, or be deemed to be, the “Beneficial Owner” of, or shall be deemed to “beneficially own,” any securities as a result of any Exempt Event.”

     (c) The definition of “Final Expiration Date” in Section 1 of the Rights Agreement is amended to read in its entirety as follows:

“Final Expiration Date” shall mean the earlier to occur of (1) the Board Appointment Date, as that term is defined in the Merger Agreement, or (2) June 6, 2012.”

     (d) The following definitions shall be added, in alphabetical order, in Section 1 of the Rights Agreement:

“Acquisition” shall mean Whitehall Acquisition Corp., a Texas corporation and a wholly owned subsidiary of Parent, formed by Parent in connection with its proposed acquisition of the Company.

“Exempt Event” shall have the meaning set forth in the definition of “Acquiring Person” set forth in this Section 1.

“Mergers” shall have the meaning set forth in definition of such term in the Merger Agreement.

“Merger Agreement” shall mean the Agreement and Plan of Merger dated as of June 3, 2008 entered into by and among the Company, Parent and Acquisition as the same may be amended from time to time.

“Offer” shall have the meaning set forth in definition of such term in the Merger Agreement.

“Parent” shall mean Smith International, Inc., a Delaware corporation.

“Top-Up Option” shall have the meaning set forth in definition of such term in the Merger Agreement.

     (e) Section 2 of the Rights Agreement is amended to add the following language at the end thereof:

“, upon ten (10) days’ prior written notice to the Rights Agent. The Rights Agent shall have no duty to supervise, and shall in no event be liable for, the acts or omissions of any such Co-Rights Agent.”

     (f) Section 3(a) of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, neither a Shares Acquisition Date nor a Distribution Date shall be deemed to have occurred as the result of any Exempt Event.”

     (g) Section 7(a) of the Rights Agreement is amended to read in its entirety as follows:

“The registered holder of any Right Certificate may exercise the Rights evidenced thereby (except as otherwise provided herein), in whole or in part, at any time after the Distribution Date, upon surrender of the Right Certificate, with the form of election to purchase on the reverse side thereof duly executed, to the Rights Agent at the principal office of the Rights Agent, together with payment of the Purchase Price for each one one-hundredth of a Preferred Share as to which the Rights are exercised, at or prior to the earliest of (i) the Close of Business on the Final Expiration Date, (ii) the time at which the Rights are redeemed as provided in Section 23 hereof (the “Redemption Date”), or (iii) the time at which such Rights are exchanged as provided in Section 24 hereof. Notwithstanding anything to the contrary in this Agreement, no Exempt Event shall be, or be deemed to be, an event that causes the Rights to become exercisable under the provisions of this Section 7 or otherwise and this Section 7 shall not apply to any Exempt Event.”

     (h) Section 11(a)(ii) of the Rights Agreement is amended by adding the following sentence at the end thereof:

“Notwithstanding anything to the contrary in this Agreement, no Exempt Event shall constitute, or be deemed to constitute, an event of the type described in this Section 11(a)(ii) and this Section 11 shall not apply to any Exempt Event.”

     (i) Section 13 of the Rights Agreement is amended by adding the following sentence at the end thereof:

“Notwithstanding anything to the contrary in this Agreement, no Exempt Event shall be, or be deemed to be, an event of the type described in this Section 13 and this Section 13 shall not apply to any Exempt Event.”

     (j) Section 18 of the Rights Agreement is amended by deleting the term “negligence” in the second sentence thereof and replace it with “gross negligence.”

     (k) Section 20(c) of the Rights Agreement is amended by deleting the term “negligence” and replace it with “gross negligence.”

     (l) Section 21 of the Rights Agreement is amended to add the following new sentence after the existing first sentence thereof:

“In the event the transfer agency relationship in effect between the Company and the Rights Agent terminates, the Rights Agent will be deemed to have resigned automatically and be discharged from its duties under this Agreement as of the effective date of such termination, and the Company shall be responsible for sending any required notice.”

     (m) Section 21 of the Rights Agreement is further amended to add the term “, along with its Affiliates,” at the end of the fifth sentence thereof after the term “$50 million”.

     (n) Section 30 of the Rights Agreement is amended by adding the following sentence at the end thereof:

“Notwithstanding the foregoing, nothing in this Agreement shall be construed to give any registered holder of Right Certificates (or, prior to any Distribution Date, the Common Shares) any legal or equitable rights, remedy or claim under this Agreement in connection with any Exempt Event.”

     (o) Section 31 of the Rights Agreement is amended by adding the following language at the end thereof:

“except that the rights, duties and obligations of the Rights Agent shall be governed by and construed in accordance with the laws of the Commonwealth of Massachusetts.”

     (p) The Rights Agreement is amended by adding the following new section at the end thereof:

“Section 34. Force Majeure. Notwithstanding anything to the contrary contained herein, the Rights Agent shall not be liable for any delays or failures in performance resulting from acts beyond its reasonable control including, without limitation, acts of God, terrorist acts, shortage of supply, breakdowns or malfunctions, interruptions or malfunction of computer facilities, or loss of data due to power failures or mechanical difficulties with information storage or retrieval systems, labor difficulties, war, or civil unrest.”

     Section 2. Effectiveness; Termination of the Merger Agreement. This Amendment shall be effective as of the date first written above, and except as expressly set forth herein, the Rights Agreement shall remain in full force and effect in accordance with the provisions thereof on the date hereof. If for any reason the Merger Agreement is terminated in accordance with its terms, then this Amendment shall be of no further force and effect and the Rights Agreement shall remain as it existed immediately prior to the effectiveness of this Amendment. The Company agrees to notify the Rights Agent promptly in the event of the occurrence of the Board Appointment Date resulting in the Final Expiration Date prior to June 6, 2012.

     Section 3. Governing Law. This Amendment shall be governed by and construed in accordance with the law of the State of Texas applicable to contracts to be made and performed entirely within such State.

     Section 4. Agreement as Amended. The term “Agreement” as used in the Rights Agreement shall be deemed to refer to the Rights Agreement as amended hereby, and all references to the Rights Agreement shall be deemed to include this Amendment.

     Section 5. Counterparts. This Amendment may be signed in one or more counterparts, all of which shall be considered one and the same instrument.

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     IN WITNESS WHEREOF, the Company and the Rights Agents have caused this Amendment to be duly executed as of the day and year first above written.