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                                                                   EXHIBIT 10.34

                              EMPLOYMENT AGREEMENT


         EMPLOYMENT AGREEMENT, dated as of January 1, 1998 between GREY WOLF,
INC., Inc. a Texas corporation (the "Company"), and David Wehlmann (the
"Executive").

         The Company desires to employ the Executive and the Executive desires
to accept employment with the Company, on the terms and conditions of this
Agreement.

         Accordingly, the parties agree as follows:

         1.       EMPLOYMENT, DUTIES AND ACCEPTANCE.

                  1.1      Employment by the Company; Duties. The Company hereby
                           agrees to employ the Executive for a term commencing
                           on January 1, 1998, and expiring at the end of the
                           day on January 1, 1999 (such date, or later date to
                           which this Agreement is extended in accordance with
                           the terms hereof, the "Termination Date"), unless
                           earlier terminated as provided in Article 4 or unless
                           extended as provided herein (the "Term"). The Term
                           shall automatically be extended on the Termination
                           Date and each anniversary thereof for successive
                           one-year periods unless either party notifies the
                           other on or before the date 90 days prior to the
                           Termination Date that he or it desires to terminate
                           the Agreement. During the Term, the Executive shall
                           initially serve in the capacity of Senior Vice
                           President/Chief Financial Officer of the Company and
                           shall also serve in those offices and directorships
                           of subsidiary corporations or entities of the Company
                           to which he may from time to time be appointed or
                           elected. During the Term, the Executive shall devote
                           all reasonable efforts and all of his business time
                           and services to the Company, subject to the direction
                           of the Board. The Executive shall not engage in any
                           other business activities except for passive
                           investments in corporations or partnerships not
                           engaged in the oil or gas drilling or well servicing
                           business.

                  1.2      Acceptance of Employment by the Executive. The
                           Executive hereby accepts such employment and shall
                           render the services and perform the duties described
                           above.

         2.       COMPENSATION AND OTHER BENEFITS.

                  2.1      Annual Salary. The Company shall pay to the Executive
                           an annual salary at a rate of not less than
                           $165,000.00 per year (the "Annual Salary"), subject
                           to increase at the sole discretion of the Board of
                           Directors of the Company (the "Board"). The Annual
                           Salary shall


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                           be payable in accordance with the payroll policies of
                           the Company as from time to time in effect, but in no
                           event less frequently than once each month, less such
                           deductions as shall be required to be withheld by
                           applicable law and regulations.

                  2.2      Bonuses. The Executive may receive, at the sole
                           discretion of the Board, an incentive bonus with
                           respect to the fiscal years ending during the term
                           hereof (the "Incentive Bonus"), provided that an
                           Incentive Bonus, payable in respect of a fiscal year,
                           shall not exceed one-half of the Annual Salary for
                           such fiscal year.

                  2.3      Grant of Option. The Company agrees to grant the
                           Executive, pursuant to the terms of its existing
                           stock option plan or new or amended stock option
                           plans, options to acquire 65,000 shares of the
                           Company's common stock, at an exercise price equal to
                           the fair market value of such stock on the date of
                           grant. Any such stock options shall vest in five
                           equal increments over a four-year period commencing
                           on the date of grant, and shall expire ten years
                           after the date of grant. One fifth of the options
                           shall vest on February 10, 1999 and on each
                           subsequent anniversary of the date of grant until the
                           fifth anniversary at which time the options shall be
                           fully vested.

                  2.4      Vacation Policy. The Executive shall be entitled to a
                           paid vacation of three weeks during each year of the
                           Term.

                  2.5      Participation in Employee Benefit Plans. The Company
                           agrees to permit the Executive during the Term, if
                           and to the extent eligible, to participate in any
                           group life, hospitalization or disability insurance
                           plan, health program, pension plan, similar benefit
                           plan or other so-called "fringe benefits" of the
                           Company (collectively, "Benefits") which may be
                           available to other senior executives of the Company
                           on terms no less favorable to the Executive than the
                           terms offered to such other executives. The Company
                           agrees to use its best efforts to obtain immediate
                           coverage for the Executive upon the commencement of
                           the Term under its existing or newly adopted medical
                           expense and hospitalization plan for employees
                           without premium surcharge and without exclusions for
                           disclosed preexisting conditions. The Executive shall
                           cooperate with the Company in applying for such
                           coverage, including submitting to a physical exam and
                           providing all relevant health and personal data.

                  2.6      General Business Expenses. The Company shall pay or
                           reimburse the Executive for all expenses reasonably
                           and necessarily incurred by the Executive during the
                           Term in the performance of the Executive's


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                           services under this Agreement. Such payment shall be
                           made upon presentation of such documentation as the
                           Company customarily requires of its senior executive
                           employees prior to making such payments or
                           reimbursements.

                  2.7      Company Car, Cellular Telephone. The Company shall
                           provide an automobile, of the Executive's choice, to
                           be used by the Executive during the Term hereof or
                           until his employment hereunder is terminated. The
                           purchase price of the automobile shall not exceed
                           $35,000 unless increased by the Board. If requested
                           by the Executive, the Company will replace the
                           automobile with a new automobile no less frequently
                           than every three years during the Term hereof. The
                           Company shall, at its expense, pay any and all
                           expenses associated with the operation of such
                           company car, including but not limited to, collision
                           and liability insurance, maintenance and repair
                           costs, replacement parts, tires, fuel and oil. The
                           Executive may use the automobile for personal
                           purposes and, to the extent of the value of such
                           personal usage, the value thereof shall be deemed to
                           be additional compensation.

         The Company shall also furnish the Executive with a cellular telephone
of his choice and the Company shall pay all charges in connection with the use
thereof, other than charges for calls not related to Executive's duties
hereunder.

         3.       NON-COMPETITION.

                  3.1      Covenants Against Competition. The Executive
                           acknowledges that (i) the Company is currently
                           engaged in the business of owning, managing and
                           operating onshore drilling and workover rigs for its
                           own account or for others which are contracted or
                           hired for the purpose of drilling and/or workover of
                           oil or natural gas wells and from time to time
                           acquiring working or carried interests in oil and gas
                           wells in connection with, or incident to, such
                           drilling or workover activities (the "Company
                           Business"); (ii) his work for the Company will give
                           him access to trade secrets of and confidential
                           information concerning the Company; and (iii) the
                           agreements and covenants contained in this Agreement
                           are essential to protect the business and goodwill of
                           the Company. Accordingly, the Executive covenants and
                           agrees as follows:

                           3.1.1 Non-Compete. The Executive shall not during the
                           Restricted Period (as defined below) in the United
                           States or any other place where the Company and its
                           affiliates conduct operations related to the Company
                           Business, directly or indirectly (except in the
                           Executive's capacity as an officer of the Company),
                           (i) engage or participate in the Company Business;
                           (ii) enter the employ of, or render any other
                           services to, any person engaged in the Company
                           Business except as


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                           permitted hereunder; or (iii) become interested in
                           any such person in any capacity, including, without
                           limitation, as an individual, partner, shareholder,
                           lender, officer, director, principal, agent or
                           trustee except as permitted hereunder; provided,
                           however, that the Executive may own, directly or
                           indirectly, solely as an investment, securities of
                           any person traded on any national securities exchange
                           or listed on the National Association of Securities
                           Dealers Automated Quotation System if the Executive
                           is not a controlling person of, or a member of a
                           group which controls, such person and the Executive
                           does not, directly or indirectly, own 1% or more of
                           any class of equity securities, or securities
                           convertible into or exercisable or exchangeable for
                           1% or more of any class of equity securities, of such
                           person. As used herein, the "Restricted Period" shall
                           mean a period commencing on the date hereof and
                           terminating upon the first to occur of (a) the date
                           on which the Company terminates or is deemed to
                           terminate the Executive's employment without Cause,
                           (b) the date the Executive terminates or is deemed to
                           terminate his employment pursuant to Section 4.6
                           hereof, or (c) the date of termination of this
                           Agreement; provided, however, that if the Company
                           shall have terminated the Executive's employment for
                           Cause and such Cause in fact exists or if the
                           Executive shall have terminated his employment with
                           the Company in breach of the terms of this Agreement,
                           the Restricted Period shall end twelve months
                           following the termination of the Executive's
                           employment hereunder.

                           3.1.2 Confidential Information; Personal
                           Relationships. The Executive acknowledges that the
                           Company has a legitimate and continuing proprietary
                           interest in the protection of its confidential
                           information and that it has invested substantial sums
                           and will continue to invest substantial sums to
                           develop, maintain and protect confidential
                           information. The Executive agrees that, during and
                           after the Restricted Period, the Executive shall keep
                           secret and retain in strictest confidence, and shall
                           not use for the benefit of himself or others all
                           confidential matters directly relating to the Company
                           Business including, without limitation, financial
                           information, trade secrets, customer lists, details
                           of client or consultant contracts, pricing policies,
                           operational methods, marketing plans or strategies,
                           product development techniques or plans, business
                           acquisition plans, new personnel acquisition plans,
                           technical processes, designs and design projects,
                           inventions and research projects of the Company, its
                           affiliates, or any other entity which may hereafter
                           become an affiliate thereof, learned by the Executive
                           heretofore or hereafter unless otherwise in the
                           public domain other than as a result of disclosure by
                           the Executive or unless independently obtained from
                           third parties not under disclosure restrictions in
                           favor of the Company.


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                           3.1.3 Property of the Company. All memoranda, notes,
                           lists, records, engineering drawings, technical
                           specifications and related documents and other
                           documents or papers (and all copies thereof) relating
                           to the Company, including such items stored in
                           computer memories, microfiche or by any other means,
                           made or compiled by or on behalf of the Executive
                           after the date hereof, or made available to the
                           Executive after the date hereof relating to the
                           Company, its affiliates or any entity which may
                           hereafter become an affiliate thereof, shall be the
                           property of the Company, and shall be delivered to
                           the Company promptly upon the termination of the
                           Executive's employment with the Company or at any
                           other time upon request; provided, however, that
                           Executive's address books, diaries, chronological
                           correspondence files and rolodex files shall be
                           deemed to be property of the Executive.

                           3.1.4 Original Material. The Executive agrees that
                           any inventions, discoveries, improvements, ideas,
                           concepts or original works of authorship relating
                           directly to the Company Business, including without
                           limitation computer systems, programs and
                           manufacturing techniques, whether or not protectable
                           by patent or copyright, that have been originated,
                           developed or reduced to practice by the Executive
                           alone or jointly with others during the Executive's
                           employment with the Company shall be the property of
                           and belong exclusively to the Company. The Executive
                           shall promptly and fully disclose to the Company the
                           origination or development by the Executive of any
                           such material and shall provide the Company with any
                           information that it may reasonably request about such
                           material.

                           3.1.5 Employees of the Company and its Affiliates.
                           During the Restricted Period, the Executive shall
                           not, directly or indirectly, hire or solicit, or
                           cause others to hire or solicit, for employment by
                           any person other than the Company or any affiliate or
                           successor thereof, any employee of the Company and
                           its affiliates or successors or encourage any such
                           employee to leave his employment.

                           3.1.6 Customers of the Company. During the Restricted
                           Period, the Executive shall not, except by reason of
                           and in his capacity as an officer of the Company,
                           directly or indirectly, request or advise a customer
                           of the Company or its subsidiaries to curtail or
                           cancel such customer's business relationship with the
                           Company.


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                  3.2      Rights and Remedies Upon Breach. If the Executive
                           breaches, or threatens to commit a breach of, any of
                           the provisions contained in Section 3.1 of this
                           Agreement (the "Restrictive Covenants"), the Company
                           shall have the following rights and remedies, each of
                           which rights and remedies shall be independent of the
                           others and severally enforceable, and each of which
                           is in addition to, and not in lieu of, any other
                           rights and remedies available to the Company under
                           law or in equity:

                           3.2.1 Specific Performance. The right and remedy to
                           have the Restrictive Covenants specifically enforced
                           by any court of competent jurisdiction, it being
                           agreed that any breach or threatened breach of the
                           Restrictive Covenants would cause irreparable injury
                           to the Company and that money damages would not
                           provide an adequate remedy to the Company.

                           3.2.2 Accounting. The right and remedy to require the
                           Executive to account for and pay over to the Company
                           all compensation, profits, monies, accruals,
                           increments or other benefits derived or received by
                           the Executive as the result of any action
                           constituting a breach of the Restrictive Covenants.

                  3.3      Severability of Covenants. The Executive acknowledges
                           and agrees that the Restrictive Covenants are
                           reasonable and valid in duration and geographical
                           scope and in all other respects. If any court
                           determines that any of the Restrictive Covenants, or
                           any part thereof, is invalid or unenforceable, the
                           remainder of the Restrictive Covenants shall not
                           thereby be affected and shall be given full effect
                           without regard to the invalid portions.

                  3.4      Blue-Pencilling. If any court determines that any of
                           the Restrictive Covenants, or any part thereof, is
                           unenforceable because of the duration or geographical
                           scope of such provision, such court shall have the
                           power to reduce the duration or scope of such
                           provision, as the case may be, and, in its reduced
                           form, such provision shall then be enforceable.

                  3.5      Enforceability in Jurisdictions. The Company and the
                           Executive intend to and hereby confer jurisdiction to
                           enforce the Restrictive Covenants upon the courts of
                           any jurisdiction within the geographical scope of
                           such Restrictive Covenants. If the courts of any one
                           or more of such jurisdictions hold the Restrictive
                           Covenants unenforceable by reason of the breadth of
                           such scope or otherwise, it is the intention of the
                           Company that such determination not bar or in any way
                           affect the right


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                           of the Company to the relief provided above in the
                           courts of any other jurisdiction within the
                           geographical scope of such Restrictive Covenants, as
                           to breaches of such Restrictive Covenants in such
                           other respective jurisdictions, such Restrictive
                           Covenants as they relate to each jurisdiction being,
                           for this purpose, severable into diverse and
                           independent covenants.

         4.       TERMINATION.

                  4.1      Termination Upon Death. If the Executive dies during
                           the Term, this Employment Agreement shall terminate,
                           provided, however, that in any such event, the
                           Company shall pay to the Executive, or to his estate,
                           any portion of the Annual Salary that shall have been
                           earned by the Executive prior to the termination but
                           not yet paid, any Benefits that have vested in the
                           Executive at the time of such termination as a result
                           of his participation in any of the Company's benefit
                           plans shall be paid to the Executive, or to his
                           estate or designated beneficiary, in accordance with
                           the provisions of such plan; and the Company shall
                           reimburse the Executive, or his estate, for any
                           expenses with respect to which the Executive is
                           entitled to reimbursement pursuant to Section 2.6 of
                           this Agreement, and the Executive's right to
                           indemnification, payment or reimbursement pursuant to
                           Section 6 of this Agreement shall not be affected by
                           such termination and shall continue in full force and
                           effect, both with respect to proceedings that are
                           threatened, pending or completed at the date of such
                           termination and with respect to proceedings that are
                           threatened, pending or completed after that date.

                  4.2      Termination With Cause. The Company has the right, at
                           any time during the Term, subject to all of the
                           provisions hereof, exercisable by serving notice,
                           effective on or after the date of service of such
                           notice as specified therein, to terminate the
                           Executive's employment under this Agreement and
                           discharge the Executive with Cause. If such right is
                           exercised, the Company's obligation to the Executive
                           shall be limited solely to the payment of unpaid
                           Annual Salary accrued, together with unpaid Incentive
                           Bonus, if any, and Benefits vested up to the
                           effective date specified in the Company's notice of
                           termination. As used in this Agreement, the term
                           "Cause" shall mean and include (i) chronic alcoholism
                           or controlled substance abuse as determined by a
                           doctor mutually acceptable to the Company and the
                           Executive, (ii) an act of proven fraud or dishonesty
                           on the part of the Executive with respect to the
                           Company or its subsidiaries; (iii) knowing and
                           material failure by the Executive to comply with
                           material applicable laws and regulations


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                           relating to the business of the Company or its
                           subsidiaries; (iv) the Executive's material and
                           continuing failure to perform (as opposed to
                           unsatisfactory performance) his duties hereunder or a
                           material breach by the Executive of this Agreement
                           except, in each case, where such failure or breach is
                           caused by the illness or other similar incapacity or
                           disability of the Executive; or (v) conviction of a
                           misdemeanor involving moral turpitude or a felony.
                           Prior to the effectiveness of termination for Cause
                           under subclause (i), (ii), (iii) or (iv) above, the
                           Executive shall be given 30 days' prior notice from
                           the Board specifically identifying the reasons which
                           are alleged to constitute cause for any termination
                           hereunder and an opportunity to be heard by the Board
                           in the event Executive disputes such allegations.

                  4.3      Termination Without Cause. The Company has the right,
                           at any time during the Term, subject to all of the
                           provisions hereof, exercisable by serving notice,
                           effective on or after the date of service of such
                           notice as specified therein, to terminate the
                           Executive's employment under this Agreement and
                           discharge the Executive without Cause. If the
                           Executive is terminated during the Term without Cause
                           (including any termination which is deemed to be a
                           constructive termination without Cause under Section
                           4.6 hereof), the Company's obligation to the
                           Executive shall be limited solely to the payment, at
                           the times and upon the terms provided for herein, of
                           the greater of (i) the Executive's Annual Salary and
                           Incentive Bonus for the number of full months
                           remaining in the Term of this Agreement (assuming no
                           automatic extension of the Term) had the Executive
                           not been so terminated and (ii) the Executive's
                           Annual Salary for a period of twelve months, in each
                           case based on the Annual Salary of the Executive in
                           effect on the date of termination (or, if the Company
                           has reduced the Executive's Annual Salary in breach
                           of this Agreement, the Executive's Annual Salary
                           before such reduction) and, in the case of clause
                           (i), the average Incentive Bonus received by the
                           Executive for the immediately preceding two fiscal
                           years, together with all unpaid Incentive Bonus and
                           Benefits awarded or accrued up to the date of
                           termination. If the Executive is terminated after he
                           has received one Incentive Bonus but before he has
                           received two, the Incentive Bonus in clause (i) shall
                           be based on the amount of that one Incentive Bonus;
                           if he has not yet received an Incentive Bonus, it
                           shall be based on the maximum Incentive Bonus (i.e.,
                           one half of the Annual Salary). In the event of a
                           termination by the Company without Cause within 180
                           days after a Change of Control (as hereinafter
                           defined), including a constructive termination
                           without Cause pursuant to Section 4.6, the amounts
                           due to


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                           the Executive pursuant to this Section 4.3 shall be
                           due and payable in one lump-sum payment within 60
                           days after such termination. In all other cases, any
                           amounts due to the Executive pursuant to this Section
                           4.3 shall be due and payable as and when they would
                           have become due and payable absent such termination.

                  4.4      Termination by the Executive. Any termination of this
                           Agreement by the Executive during the Term, except
                           such termination as is deemed to be a constructive
                           termination without Cause by the Company under
                           Section 4.6 of this Agreement, shall be deemed to be
                           a breach of the terms of this Agreement for the
                           purposes of Section 3.1.1 hereof and shall entitle
                           the Company to discontinue payment of all Annual
                           Salary, Incentive Bonuses and Benefits accruing from
                           and after the date of such termination.

                  4.5      Termination upon Disability. If during the Term the
                           Executive becomes physically or mentally disabled,
                           whether totally or partially, as evidenced by the
                           written statement of a competent physician licensed
                           to practice medicine in the United States who is
                           mutually acceptable to the Company and the Executive
                           or his closest relative if he is not then able to
                           make such a choice, so that the Executive is unable
                           substantially to perform his services hereunder for
                           (i) a period of four consecutive months, or (ii) for
                           shorter periods aggregating six months during any
                           twelve-month period, the Company may at any time
                           after the last day of the four consecutive months of
                           disability or the day on which the shorter periods of
                           disability equal an aggregate of six months, by
                           written notice to the Executive, terminate the
                           Executive's employment hereunder and discontinue
                           payments of the Annual Salary, Incentive Bonuses and
                           Benefits accruing from and after the date of such
                           termination. The Executive shall be entitled to the
                           full compensation payable to him hereunder for
                           periods of disability shorter than the periods
                           specified in clauses (i) and (ii) of the previous
                           sentence.

                  4.5      Constructive Termination Without Cause.
                           Notwithstanding any other provision of this
                           Agreement, the Executive's employment under this
                           Agreement may be terminated during the Term by the
                           Executive, which shall be deemed to be constructive
                           termination by the Company without Cause, if one of
                           the following events shall occur without the consent
                           of the Executive: (i) a failure to elect or reelect
                           or to appoint or reappoint the Executive to the
                           office of Senior Vice President/Chief Financial
                           Officer of the Company or other material change by
                           the Company of the Executive's functions, duties or
                           responsibilities which change would reduce the
                           ranking or level, dignity, responsibility, importance
                           or scope of the Executive's position with the Company
                           from the position and attributes thereof described in
                           Section 1 above; (ii) the assignment or reassignment
                           by the Company of the Executive to


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                           another place of employment more than 50 miles from
                           the Executive's principal place of residence in the
                           Houston, Texas, metropolitan area; (iii) the
                           liquidation, dissolution, consolidation or merger of
                           the Company, or transfer of all or substantially all
                           of its assets, other than a transaction in which a
                           successor corporation with a net worth at least equal
                           to that of the Company assumes this Agreement and all
                           obligations and undertakings of the Company
                           hereunder; (iv) a reduction in the Executive's fixed
                           salary; (v) a Change of Control as hereinafter
                           defined; (vi) the failure of the Company to continue
                           to provide the Executive with office space, related
                           facilities and secretarial assistance that are
                           commensurate with the Executive's responsibilities to
                           and position with the Company; (vii) the notification
                           by the Company of the Company's intention not to
                           observe or perform one or more of the obligations of
                           the Company under this Agreement; (viii) the failure
                           by the Company to indemnify, pay or reimburse the
                           Executive at the time and under the circumstances
                           required by Section 6 of this Agreement; (ix) the
                           occurrence of any other material breach of this
                           Agreement by the Company or any of its subsidiaries;
                           or (x) the delivery of notice by the Company in
                           accordance with Section 1.1 hereof that it desires to
                           terminate the Agreement, but only if such notice is
                           given before the Term has been automatically extended
                           three times. Any such termination shall be made by
                           written notice to the Company, specifying the event
                           relied upon for such termination and given within 60
                           days after such event. Any constructive termination
                           shall be effective 60 days after the date the Company
                           has been given such written notice setting forth the
                           grounds for such termination with specificity;
                           provided, however, that Executive shall not be
                           entitled to terminate this Agreement in respect of
                           any of the grounds set forth above if within 60 days
                           after such notice the action constituting such ground
                           for termination is no longer continuing. A
                           constructive termination by the Company without Cause
                           shall terminate the Restrictive Period hereunder.

                  4.7      For the purposes hereof, a "Change of Control of the
                           Company" shall be deemed to have occurred if after
                           the effective date (i) any "person" (as such term is
                           used in Sections 13(d) and 14(d) of the Act) is or
                           becomes the "beneficial owner" (as defined in Rule
                           13d-3 under the Securities Exchange Act of 1934 (the
                           "Act")), directly or indirectly, of securities of the
                           Company representing 50% or more of the combined
                           voting power of the Company's then outstanding
                           securities without the prior approval of at least a
                           majority of the members of the Board in office
                           immediately prior to such person attaining such
                           percentage interest; (ii) there occurs a proxy
                           contest or a consent solicitation, or the Company is
                           a party to a merger, consolidation, sale of assets,
                           plan


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                           of liquidation or other reorganization not approved
                           by at least a majority of the members of the Board in
                           office, as a consequence of which members of the
                           Board in office immediately prior to such transaction
                           or event constitute less than a majority of the Board
                           thereafter; or (iii) during any period of two
                           consecutive years, other than as a result of an event
                           described in clause (ii) of this Section 4.7,
                           individuals who at the beginning of such period
                           constituted the Board (including for this purpose any
                           new director whose election or nomination for
                           election by the Company's stockholders was approved
                           by a vote of at least a majority of the directors
                           then still in office who were directors at the
                           beginning of such period) cease for any reason to
                           constitute at least a majority of the Board.

         5.       INSURANCE.

         The Company may, from time to time, apply for and take out, in its own
         name and at its own expense, naming itself or one or more of its
         affiliates as the designated beneficiary (which it may change from time
         to time), policies for life, health, accident, disability or other
         insurance upon the Executive in any amount or amounts that it may deem
         necessary or appropriate to protect its interest. The Executive agrees
         to aid the Company in procuring such insurance by submitting to medical
         examinations and by filling out, executing and delivering such
         applications and other instruments in writing as may reasonably be
         required by an insurance company or companies to which any application
         or applications for insurance may be made by or for the Company.

6.       INDEMNIFICATION.

         6.1      The Company shall, to the extent not prohibited by law,
                  indemnify the Executive if he is made, or threatened to be
                  made, a party to any threatened, pending or completed action,
                  suit or proceeding, whether civil, criminal, administrative or
                  investigative, including an action by or in the right of the
                  Company to procure a judgment in its favor (hereinafter a
                  "Proceeding"), by reason of the fact that the Executive is or
                  was a director or officer of the Company, or is or was serving
                  in any capacity at the request of the Company for any other
                  corporation, partnership, joint venture, trust, employee
                  benefit plan or other enterprise, against judgments, fines,
                  penalties, excise taxes, amounts paid in settlement and costs,
                  charges and expenses (including attorneys' fees and
                  disbursements) paid or incurred in connection with any such
                  Proceeding.


                                      -11-
<PAGE>   12

         6.2      The Company shall, from time to time, reimburse or advance to
                  the executive the funds necessary for payment of expenses,
                  including attorneys' fees and disbursements, incurred in
                  connection with any Proceeding in advance of the final
                  disposition of such Proceeding; provided, however, that, if
                  required by the Texas Business Corporation Act, such expenses
                  incurred by or on behalf of the Executive may be paid in
                  advance of the final disposition of a Proceeding only upon
                  receipt by the Company of an undertaking, by or on behalf of
                  the Executive, to repay any such amount so advanced if it
                  shall ultimately be determined by final judicial decision from
                  which there is no further right of appeal that the Executive
                  is not entitled to be indemnified for such expenses.

         6.3      The right to indemnification and reimbursement or advancement
                  of expenses provided by, or granted pursuant to, this Article
                  6 shall not be deemed exclusive of any other rights which the
                  Executive may now or hereafter have under any law, by-law,
                  agreement, vote of stockholders or disinterested directors or
                  otherwise, both as to action in his official capacity and as
                  to action in another capacity while holding such office.

         6.4      The right to indemnification and reimbursement or advancement
                  of expenses provided by, or granted pursuant to, this Article
                  6 shall continue as to the Executive after he has ceased to be
                  a director or officer and shall inure to the benefit of the
                  heirs, executors and administrators of the Executive.

         6.5      The Company shall purchase and maintain director and officer
                  liability insurance on such terms and providing such coverage
                  as the Board determines is appropriate, and the Executive
                  shall be covered by such insurance on the same basis as the
                  other directors and executive officers of the Company.

         6.6      The right to indemnification and reimbursement or advancement
                  of expenses provided by, or granted pursuant to, this Article
                  6 shall be enforceable by the Executive in any court of
                  competent jurisdiction. The burden of proving that such
                  indemnification or reimbursement or advancement of expenses is
                  not appropriate shall be on the Company. Neither the failure
                  of the Company (including its board of directors, independent
                  legal counsel, or its stockholders) to have made a
                  determination prior to the commencement of such action that
                  such indemnification or reimbursement or advancement of
                  expenses is proper in the circumstances nor an actual
                  determination by the Company (including its board of
                  directors, independent legal counsel, or its stockholders)
                  that the Executive is not entitled to such


                                      -12-
<PAGE>   13


                  indemnification or reimbursement or advancement of expenses
                  shall constitute a defense to the action or create a
                  presumption that the Executive is not so entitled. The
                  Executive shall also be indemnified for any expenses incurred
                  in connection with successfully establishing his right to such
                  indemnification or reimbursement or advancement of expenses,
                  in whole or in part, in any such proceeding.

         6.7      If the Executive serves (1) another corporation of which a
                  majority of the shares entitled to vote in the election of its
                  directors is held by the Company, or (2) any employee benefit
                  plan of the Company or any corporation referred to in clause
                  (1), in any capacity, then he shall be deemed to be doing so
                  at the request of the Company.

         6.8      The right to indemnification or reimbursement or advancement
                  of expenses shall be interpreted on the basis of the
                  applicable law in effect at the time of the occurrence of the
                  event or events giving rise to the applicable Proceeding.


7.       OTHER PROVISIONS.

         7.1      Certain Definitions. As used in this Agreement, the following
                  terms have the following meanings unless the context otherwise
                  requires:

                  (i)      "affiliate" with respect to the Company means any
                           other person controlled by or under common control
                           with the Company but shall not include any
                           stockholder or director of the Company, as such.

                  (ii)     "person" means any individual, corporation,
                           partnership, firm, joint Company, association,
                           joint-stock company, trust, unincorporated
                           organization, governmental or regulatory body or
                           other entity.

                  (iii)    "subsidiary" means any corporation 50% or more of the
                           voting securities of which are owned directly or
                           indirectly by the Company.

         7.2      Notices. Any notice or other communication required or
                  permitted hereunder shall be in writing and shall be delivered
                  personally, telegraphed, telexed, sent by facsimile
                  transmission or sent by certified, registered or express mail,
                  postage prepaid. Any such notice shall be deemed given when so
                  delivered personally, telegraphed, telexed or sent by
                  facsimile transmission or, if mailed, on the date of actual
                  receipt thereof, as follows:


                                      -13-
<PAGE>   14

                  (i)      IF TO THE COMPANY, TO:

                           Grey Wolf, Inc.
                           10370 Richmond Avenue, Suite 600
                           Houston, Texas 77042

                           WITH A COPY TO:
                           Garderer Wynn Sewell & Riggs L.L.P.
                           333 Clay Avenue, Suite 800
                           Houston, Texas 77002-4086
                           Attention: Frank Putman, Esq.


                  (ii)     IF TO THE EXECUTIVE, TO:
                           David Wehlmann
                           22402 Wildwood Grove
                           Katy, Texas 77450

Any party may change its address for notice hereunder by notice to the other
party hereto.

                  7.3      Entire Agreement. This Agreement contains the entire
                           agreement between the parties with respect to the
                           subject matter hereof and supersedes all prior
                           agreements, written or oral, with respect thereto.

                  7.4      Waivers and Amendments. This Agreement may be
                           amended, superseded, canceled, renewed or extended,
                           and the terms and conditions hereof may be waived,
                           only by a written instrument signed by the parties
                           or, in the case of a waiver, by the party waiving
                           compliance. No delay on the part of any party in
                           exercising any right, power or privilege hereunder
                           shall operate as a waiver thereof. Nor shall any
                           waiver on the part of any party of any such right,
                           power or privilege hereunder, nor any single or
                           partial exercise of any right, power or privilege
                           hereunder, preclude any other or further exercise
                           thereof or the exercise of any other right, power or
                           privilege hereunder.

                  7.5      Governing Law. This Agreement shall be governed by
                           and construed in accordance with the laws of the
                           State of Texas (without giving effect to the choice
                           of law provisions thereof) where the employment of
                           the Executive shall be deemed, in part, to be
                           performed and enforcement of this Agreement or any
                           action taken or held with respect to this Agreement
                           shall be taken in the courts of appropriate
                           jurisdiction in Houston, Texas.


                                      -14-
<PAGE>   15

                  7.6      Assignment. This Agreement, and any rights and
                           obligations hereunder, may not be assigned by the
                           Executive and may be assigned by the Company (subject
                           to Section 4.6 (iii) hereof) only to a successor by
                           merger or purchasers of substantially all of the
                           assets of the Company.

                  7.7      Counterparts. This Agreement may be executed in
                           separate counterparts, each of which when so executed
                           and delivered shall be deemed an original, but all of
                           which together shall constitute one and the same
                           instrument.

                  7.8      Headings. The headings in this Agreement are for
                           reference purposes only and shall not in any way
                           affect the meaning or interpretation of this
                           Agreement.

                  7.9      No Presumption Against Interest. This Agreement has
                           been negotiated. drafted, edited and reviewed by the
                           respective parties, and therefore, no provision
                           arising directly or indirectly herefrom shall be
                           construed against any party as being drafted by said
                           party.

                  7.10     Validity Contest. The Company shall promptly pay any
                           and all legal fees and expenses incurred by the
                           Executive from time to time as a direct result of the
                           Company's contesting the due execution,
                           authorization, validity or enforceability of this
                           Agreement.

                  7.11     Binding Agreement. This Agreement shall inure to the
                           benefit of and be binding upon the Company and its
                           respective successors and assigns and the Executive
                           and his legal representatives.

         IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first above written.

                                       GREY WOLF, INC.


                                       By /s/ T. P. RICHARDS
                                          --------------------------------------
                                          Name:  T. P. Richards
                                          Title: President and CEO


                                       EXECUTIVE

                                       /s/ DAVID WEHLMANN
                                       -----------------------------------------
                                       Name:  David Wehlmann
                                       Title: Senior Vice President/Chief
                                              Financial Officer


                                      -15-