<PAGE>
                                                                   Exhibit 10.12
                           RESTRICTED STOCK AGREEMENT

      This RESTRICTED STOCK AGREEMENT (this "Agreement") is dated as of the 12th
day of May, 2004 between W-H ENERGY SERVICES, INC., a Texas corporation (the
"Company"), and KENNETH T. WHITE, JR. (the "Executive").

      WHEREAS, the Executive currently is employed by the Company as the
Company's President and Chief Executive Officer and serves as Chairman of the
Company's Board of Directors pursuant to an Employment Agreement entered into by
and between the Company and Executive on October 16, 2003 (the "Employment
Agreement"); and

      WHEREAS, in order to induce the Executive to remain with the Company and
devote his best efforts to the business of the Company, the Company has
determined to make a grant of restricted stock to the Executive; and

      WHEREAS, the shareholders of the Company approved the issuance of such
restricted stock to the Executive at the annual meeting of the Company's
shareholders held on May 12, 2004;

      NOW, THEREFORE, for and in consideration of the mutual promises, covenants
and obligations contained herein the Company and the Executive hereby agree as
follows:

      1. Issuance of Stock. By the execution of this Agreement, the Company
hereby grants to the Executive 75,000 shares of its common stock, par value
$0.0001 per share (the "Stock"). The shares of Stock issued to the Executive
under this Agreement shall be subject to all of the terms, conditions and
restrictions set forth in this Agreement.

      2. Forfeiture Restrictions. The shares of Stock issued to the Executive
pursuant to this Agreement (i) shall not be sold, assigned, pledged or otherwise
transferred to the extent then subject to the Forfeiture Restrictions (as
defined below) and (ii) the Executive shall be obligated, in the event of the
termination of the Executive's employment with the Company, to forfeit and
surrender to the Company for no consideration any shares of Stock as to which
the Forfeiture Restrictions then apply in accordance with Section 3 hereof. Such
prohibition against sale, assignment, pledge or transfer and the obligation to
forfeit and surrender shares of Stock to the Company are herein referred to as
the "Forfeiture Restrictions," and the shares of Stock which are subject to the
Forfeiture Restrictions are herein sometimes referred to as "Restricted Shares."

      3. Lapse of Forfeiture Restrictions.

      (a) The Forfeiture Restrictions shall lapse as to shares of Stock issued
to the Executive pursuant to this Agreement in accordance with the following
schedule provided that the Executive has been continuously employed by the
Company:
<PAGE>
<TABLE>
<CAPTION>
                                        Number of Shares As To Which
                                          Forfeiture Restrictions
                    Lapse Date                     Lapse
                   ------------                    ------
<S>                                     <C>
                   May 12, 2005                    25,000
                   May 12, 2006                    25,000
                   May 12, 2007                    25,000
</TABLE>

      (b) The Forfeiture Restrictions on all Restricted Shares shall lapse
immediately (i) upon a Change in Control (as defined in the Employment
Agreement) and (ii) upon the termination of the Executive's employment with the
Company; provided, however, that if the Executive's employment is terminated by
the Company for any reason encompassed by paragraph 2.2(iii) of the Employment
Agreement or by the Executive pursuant to paragraph 2.3(iii) of the Employment
Agreement, then such Forfeiture Restrictions shall not lapse, and the Executive
shall forfeit and shall be obligated to and shall surrender to the Company for
no consideration any shares of Stock as to which the Forfeiture Restrictions
then apply.

      4. Shares Received in Reorganization or Stock Split. The prohibition
against the transfer of the shares of Stock subject to the Forfeiture
Restrictions shall not apply to the exchange of Restricted Shares pursuant to a
plan of reorganization of the Company, but the stock or securities received in
exchange therefor, and any stock received as a result of a stock split or stock
dividend with respect to Restricted Shares, shall also become Restricted Shares
subject to the Forfeiture Restrictions.

      5. Endorsement on Certificate. Each certificate representing Restricted
Shares shall be conspicuously endorsed as follows:

            The sale, assignment, pledge or other transfer of the shares of
      stock evidenced by this certificate is prohibited by the terms and
      conditions of that certain Restricted Stock Agreement dated as of May 12,
      2004, a copy of which is attached hereto and incorporated herein, and such
      shares may not be sold, assigned, pledged or otherwise transferred except
      as provided in such agreement.

      6. Community Interest of Spouse. The community interest, if any, of any
spouse of the Executive in any of the Restricted Shares shall be subject to all
the terms, conditions and restrictions of this Agreement, and shall be forfeited
and surrendered to the Company upon the occurrence of any of the events
requiring the Executive's interest in such Restricted Shares to be so forfeited
and surrendered pursuant to this Agreement.

      7. Withholding of Tax. To the extent the issuance of Stock or the lapse of
Forfeiture Restrictions results in the receipt of compensation by the Executive
for tax purposes, the Company shall withhold from any cash compensation then or
thereafter payable to the Executive any tax required to be withheld by reason
thereof. To the extent the Company determines that such cash compensation is or
may be insufficient to fully satisfy such withholding requirement, the Executive
shall deliver to the Company cash in an amount determined by the Company to be
sufficient to satisfy any such withholding requirement.


                                       -2-
<PAGE>
      8. Tax Election. If the Executive makes the election authorized by section
83(b) of the Internal Revenue Code of 1986, as amended (the "Code"), the
Executive shall submit to the Company a copy of the statement filed by the
Executive to make such election.

      9. Stock Power and Retention of Certificates. The Company may require the
Executive to execute and deliver to the Company a stock power in blank with
respect to the Restricted Shares and may, in its sole discretion, determine to
retain possession of the certificates for shares of Stock with respect to which
the Forfeiture Restrictions have not lapsed. The Company shall have the right,
in its sole discretion, to exercise such stock power in the event that the
Company becomes entitled to shares of Stock pursuant to the provisions of
Section 3(b) as a result of a termination of the Executive's employment with the
Company pursuant to the proviso in clause (ii) of Section 3(b). Notwithstanding
retention of such certificates by the Company, the Executive shall have all
rights (including dividend and voting rights) with respect to the shares of
Stock represented by such certificates.

      10. Government Regulation. The Executive understands that at the time of
the execution of this Agreement, the issuance of the shares of Stock to be
issued in accordance with this Agreement has not been registered under the
Securities Act of 1933 (the "Act") or any state securities law and are being
issued pursuant to an exemption from such registration requirements. The
Executive acknowledges and agrees that the shares of Stock that he receives in
accordance with this Agreement are being acquired by the Executive for
investment purposes only and not with a view to distributing same in violation
of the Act or any state securities laws. Such shares of Stock may not be sold or
transferred in the absence of an effective registration statement under the Act
(and any applicable state securities laws) or an applicable exemption from the
registration requirements of the Act (and any applicable state securities laws),
so long as such exemption is available to the Executive in the opinion of
counsel.

      In addition, the Executive agrees (i) that the certificates representing
the shares of Stock received pursuant to this Agreement may bear such legend or
legends as the Board of Directors of the Company deems appropriate in order to
assure compliance with applicable securities laws (ii) that the Company may
instruct its transfer agent to enter stop transfer instructions with respect to
the shares of Stock received pursuant to this Agreement and (iii) that the
Company may refuse to transfer the Stock on the stock transfer records of the
Company unless such proposed transfer would not in the opinion of counsel
violate any applicable securities law.

      As a condition to the obligations of the Company under this Agreement, and
to induce the Company to enter into this Agreement, the Executive hereby
represents that, as of the date of this Agreement, (i) the Executive has such
knowledge and experience in financial and business matters that the Executive is
capable of evaluating the merits and economic risks of this particular
investment in the Stock; (ii) the Executive is able to bear the economic risk of
this particular investment in Stock; (iii) the Executive has access to such
information concerning the business and affairs of the Company as he believes is
necessary to evaluate an investment in the Stock; and (iv) the Executive further
realizes that the Company is under no obligation to register such shares of
Stock for resale by the Executive or to aid the Executive in obtaining any
exemption from the registration requirements under the Act.


                                       -3-
<PAGE>
      11. Parachute Payment. In the event that receipt of the Restricted Shares
upon the lapse of any Forfeiture Restrictions would constitute a parachute
payment (within the meaning of Section 280G of the Code) at a time when the
Employment Agreement (or any successor agreement) is in effect, then the amount
of such parachute payment shall be treated as a payment to the Executive for
purposes of determining the amount of any gross-up payment to be made to the
Executive under the terms of such Employment Agreement (or successor agreement)
with respect to the excise tax imposed by Section 4999 of the Code.

      12. Binding Effect. This Agreement shall be binding upon and inure to the
benefit of any successors to the Company and all persons lawfully claiming under
the Executive.

      13. Governing Law. This Agreement shall be governed by and construed in
accordance with the laws of the State of Texas without giving effect to any
conflict of laws rule or principle that would refer the construction of this
Agreement to the laws of another jurisdiction.

      IN WITNESS WHEREOF, the Company has executed this Agreement by its duly
authorized officer, and the Executive and his spouse have executed this
Agreement, all as of the day and year first above written.

                                          W-H ENERGY SERVICES, INC.


                                          By:   /s/ Jeffrey L. Tepera
                                              --------------------------------
                                              Jeffrey L. Tepera
                                              Vice President and Chief Financial
                                              Officer

                                          KENNETH T. WHITE, JR.


                                                /s/ Kenneth T. White, Jr.
                                          ------------------------------------


                                          MARLAINE WHITE


                                                /s/ Marlaine White
                                          ------------------------------------


                                       -4-