<PAGE>

                                                                   EXHIBIT 10.29

                                 EMPLOYMENT AGREEMENT


          THIS IS AN EMPLOYMENT AGREEMENT (the "Agreement") between MILLER
EXPLORATION COMPANY, a Delaware corporation ("Company") and Lew P. Murray
("Employee").  The parties agree as follows:

    1.   Effective Date and Term. This Agreement will take effect as of February
9, 1998. The initial term of this Agreement will be three (3) years following
its effective date. If the Employment terminates at any time before expiration
of this Agreement, then notwithstanding such expiration the parties will remain
obligated to comply with their respective obligations under Paragraph 6. The
Employee's obligations and the Company's rights under Paragraphs 8, 9 and 10
shall survive expiration of this Agreement, and shall continue in full force and
effect.

    2.   Employment. The Employee will serve as Vice President of Exploration of
the Company, or in other positions assigned by the Company (the "Employment").
The Employee's duties will be those assigned by the Company's Board of Directors
or the President or Chief Executive Officer, as the case may be. The Employment
will be full time, and the Employee's entire business time and best efforts will
be devoted to the performance of Employee's duties for the Company during the
term of the Employment, provided that, except as otherwise provided in this
Agreement, nothing in this Paragraph shall prevent the Employee from engaging in
additional activities in connection with personal investments and community
affairs that do not compromise the Company's assets and are not inconsistent
with the Employee's duties under this Agreement. Employee will comply with the
Company's employment policies.

    3.   Termination of Employment.  During the term of this Agreement, the
Employment may be terminated as provided in Paragraph 5.  After expiration of
this Agreement, either party may terminate the Employment at will.

    4.   Compensation.  The Employee will be compensated during the Employment
as follows:

         a.  Salary.  The Employee will be paid an initial annual salary of at
    least $140,000, subject to adjustment as provided below, which will be
    payable in equal periodic installments according to the Company's customary
    payroll practices, but no less frequently than monthly. The Employee's
    salary will be reviewed by the Company's Compensation Committee not less
    frequently than annually, and may be adjusted upward or downward in the sole
    discretion of the Board of Directors, but in no event will the salary be
    less than $112,000 per year, except upon approval of employee.

          b.  Stock Options.  Employee has been granted options to purchase
    100,000 shares of the Company's common stock at the initial public offering
    price of $8.00 per share. The options will have a 10-year term and will
    vest in cumulative annual increments of one-fifth of the total number of
    shares subject to the options,
<PAGE>

    beginning on the first anniversary of the date of grant (February 4, 1999).
    The options have been granted pursuant to a separate stock option agreement
    between the Company and Employee, and the options will be subject to any
    restrictions and other terms set forth in that agreement and in any plan
    under which the options may be granted, including the Company's Stock Option
    and Restricted Stock Plan of 1997. In addition, the stock and other stock
    options granted in the future, will vest upon a Change in Control of the
    Company, as defined in Paragraph 15, (which definition shall modify and
    supersede any definition of a "Change in Control" or comparable term in the
    stock option plan or the agreement referenced in the preceding sentence.)
    Employee may participate in future option programs as determined by the
    Board of Directors.

          c.  Restricted Stock.  Employee has been issued 15,000 shares of
    restricted common stock that will vest in cumulative annual increments of
    one-half of the total number of restricted shares granted, beginning on the
    first anniversary of the date of grant. In addition, the stock and other
    restricted stock granted in the future, will vest upon a change in control
    of the Company, as referenced in Paragraph 15, (which definition shall
    modify and supersede any definition of a "Change in Control" or comparable
    term in the restricted stock plan or the agreement referenced in the
    following sentence.) The restricted stock has been granted pursuant to the
    Company's Stock Option and Restricted Stock Plan of 1997 agreement between
    the Company and Employee, and the restricted stock will be subject to any
    restrictions and other terms set forth in that agreement and in any plan
    under which the restricted stock may be granted, including the Company's
    Stock Option and Restricted Stock Plan of 1997. Employee may participate in
    future restricted stock programs as determined by the Board of Directors.

          d.  Bonus.  The Employee will be eligible to participate in any bonus
    program covering the position in which the Employee serves, on the terms set
    forth in such bonus program. The terms of any present or future bonus
    programs are subject to revision from time to time in the Company's
    discretion.

          e.  Benefits. The Employee will, during the term of Employment, be
    permitted to participate in such pension, 401(k), profit sharing, life
    insurance, health insurance, and other employee benefit plans of the Company
    that may be in effect from time to time, to the extent the Employee is
    eligible under the terms of those plans (collectively, the "Benefits"). In
    addition, Employee will be eligible to receive twenty (20) days of vacation.

          f.  Business Expenses.  The Company will reimburse the Employee for
    reasonable ordinary and necessary business expenses incurred in the
    performance of duties on behalf of the Company, subject to Employee's
    prompt submission of proper

                                   2 of 13
<PAGE>

    documentation for tax and accounting purposes and, if applicable, subject
    to the approval of the respective Supervisor.

        g.  Plan Terms and Changes.  The terms of applicable insurance
    policies and benefit plans in effect from time to time will govern with
    regard to specific issues of coverage and benefit eligibility. It is
    understood that all benefit programs are subject to change or cancellation
    in the discretion of the Company.

    5.  Termination of Employment. During the term of this Agreement, Employee's
Employment may be terminated in the following circumstances:

        a.  Death.  The Employment will terminate automatically in the event
    of Employee's death.

        b.  Disability.  If Employee becomes "disabled", the Company may elect
    to terminate Employee's Employment due to such disability. For the purposes
    of this Agreement, the Employee will be deemed to be "disabled" if the
    Employee is unable to perform the essential functions of the Employee's
    duties under this Agreement, due to physical or mental illness, for 120
    consecutive days, or 180 days during any twelve-month period, as determined
    in accordance with this Paragraph. The disability of the Employee will be
    determined by a medical doctor selected by written agreement of the Company
    and the Employee upon the request of either party by notice to the other. If
    the Company and the Employee cannot agree on the selection of a medical
    doctor, each of them will select a medical doctor and the two medical
    doctors will select a third medical doctor who will determine whether the
    Employee is disabled. The determination of the medical doctor selected under
    this Paragraph will be binding on both parties.

        c.   Termination by Company for Cause.  The Company may terminate the
    Employment immediately for Cause, defined as Employee's: (i) material breach
    of this Agreement, including but not limited to, continued poor performance
    of duties after warning and reasonable opportunity to correct performance
    deficiencies; (ii) willful failure to substantially perform properly
    assigned job duties; (iii) misappropriation of Company property, intentional
    damage to Company property, activities in aid of a competitor,
    insubordination, conviction of a crime involving moral turpitude, or
    performance of any act (including any dishonest or fraudulent act or
    statement) that is willfully detrimental to the interests of the Company.

        d.  Termination by Employee for Good Reason.  Employee may terminate
    the Employment for Good Reason if:


             (i)  Either

                                    3 of 13
<PAGE>

                    (A)  the Company materially breaches its obligations to
                         Employee under this Agreement; or
                    (B)  the Company fails to assign or a Successor fails to
                         assume this Agreement as provided in Paragraph 14; or
                         the Successor reduces Employee's salary, reduces
                         Employee's bonus opportunity, or materially reduces the
                         overall value of Employee's fringe benefits.

               (ii)  Employee notifies the Board of Directors in writing, within
          60 days after the act or omission in question, asserting that the act
          or omission in question constitutes Good Reason and explaining why
          such act or omission constitutes a material breach; and

               (iii) the Company fails, within 30 days after such notification,
          to take all steps necessary to cure the breach; and

               (iv)  Employee resigns by written notice within 30 days after
          expiration of the 30 day period under (iii) above.

          If Employee terminates the Employment for Good Reason, Employee will
     be paid Severance Pay as provided in Paragraph 6.  Employee's failure to
     object to a material breach as provided above will not waive Employee's
     right to resign with Good Reason after following the above procedure with
     regard to any future material breach.

          e.  Discretionary Termination by Employee.  Employee may terminate the
     Employment at will, with at least 45 days advance written notice, and
     Employee agrees not to leave the Employment with Company without giving
     such notice.

          f.  Discretionary Termination by Company.  Company may terminate the
     Employee's Employment at will, but if it does so it will pay Employee
     Severance Pay as provided in Paragraph 6.

          Employee agrees to cooperate during the 90-day period following any
termination of the Employment by consulting upon request to assist in
transition of Employee's duties and knowledge about the Company's business, such
consulting to be performed at Employee's reasonable convenience by telephone,
and the Company agrees to pay a consulting fee computed as Employee's weekly
salary divided by 40 for each hour of consultation (unless Employee is receiving
Severance Pay under Paragraph 6).

      6.  Payments After Termination of Employment.


                                    4 of 13
<PAGE>

          a.  Upon termination of Employee's Employment, Employee shall not be
     entitled to any further compensation from Company or any Affiliate, except:
     (i) unpaid salary installments through the end of the week in which the
     Employment terminates; and (ii) any vested benefits accrued prior to the
     date the Employment terminates under the terms of any written Company
     benefit plan that expressly calls for payments or rights after termination
     of employment;  (iii) COBRA continuation coverage at Employee's expense, if
     Employee is eligible under applicable law; and (iv) Severance Pay (if any)
     becoming due under Paragraph 6 or Paragraph 15.

          b.  The Company will pay Employee the Severance Pay described in this
     Paragraph if the Company terminates the Employee's Employment during the
     term of this Agreement other than as permitted under Paragraph 5(b)
     ("Disability") or 5(c) ("Cause"), except that no Severance Pay will be
     owing from the Company  by reason of the sale of the Company's business, if
     this Agreement is assigned to and assumed by a Successor Company, as
     provided in Paragraph 14.  A purported termination of the Employment under
     Paragraph 5(c) ("Termination by Company for Cause") or Paragraph 5(b)
     ("Disability") that is ultimately found to have been improper under such
     paragraph shall be deemed to have been a termination under Paragraph 5(f)
     ("Discretionary Termination by Company").  The Company will also pay
     Employee the Severance Pay described in this Paragraph if the Employee
     terminates his Employment during the term of this Agreement for Good
     Reason, as provided in Paragraph 5(d) ("Termination by Employee for Good
     Reason").

          c.  Amount and Duration of Severance Pay.  Subject to the other
     provisions of this Paragraph 6, the Severance Pay will consist of:

               (i)  continuation of Employee's initial weekly salary (or current
          salary, whichever is greater) for 26 weeks;

               (ii) continuation during the Severance Pay Period, at Company's
          expense, of Employee's existing benefits employee and dependent
          health, dental and prescription drug coverage, life insurance if
          possible under the policy for the remaining term of this Agreement
          (without affecting Employee's right to elect COBRA continuation
          coverage beginning on the expiration date of this Agreement), subject
          to Employee's continuing payment of the normal employee contribution;
          and

               (iii)  if Employee dies during Severance Pay period, Severance
          Pay will continue for the benefit of the Employee's designated
          beneficiary.

          In addition, upon Employee's becoming entitled to Severance Pay, all
     options and restricted stock previously granted to Employee will vest.


                                    5 of 13
<PAGE>

          d.  Conditions to Severance Pay.  In order to be eligible for the
     Severance Pay, Employee must meet the following conditions:

               (i)   Employee must comply with Employee's obligations under
          Paragraphs 8, 9 and 10 of this Agreement;

               (ii)  Employee must not claim unemployment compensation for any
          week for which Employee receives Severance Pay;

               (iii) Employee must promptly sign and continue to honor a
          general release form acceptable to the Company and Employee of any and
          all claims against Company and its affiliates (defined for purposes of
          this Agreement as entities having an ownership interest in the
          Company, and subsidiaries and other entities in which the Company has
          an ownership interest), and all of their officers, directors,
          employees and agents.  The release will not waive the Employee's right
          to any payments due under this Paragraph 6 or Employee's rights to any
          vested benefits accrued prior to the date of termination of Employment
          under the terms of the applicable written benefit plans of the
          Company, or any right of Employee to indemnification or liability
          insurance coverage or Employee's rights to previously granted stock
          options and/or restricted stock.  If Employee ever seeks to make a
          claim against the Company contrary to the general release, it is
          understood that Employee must return the severance pay to company
          before doing so.  If the company successfully enforces the general
          release, the Severance Pay will be returned to the Employee less the
          Company's cost of enforcement.

               (iv)  Employee must resign, upon written request by Company, from
          all positions with or representing Company or any Affiliate, including
          but not limited to membership on boards of directors; and

               (v)   Employee must provide the Company during the Severance Pay
          Period (without additional compensation) with consulting services
          regarding matters within the scope of Employee's former duties, upon
          request by the Board of Directors, provided that Employee will only be
          required to provide such services by telephone at Employee's
          reasonable convenience, and not for more than forty (40) hours in any
          month.

          e.  Offsets to Severance Pay.  The Severance Pay due to Employee for
     any week will be reduced by any disability benefits received by Employee
     for the same period under any Workmen's Compensation law, or under the
     Federal Social Security act Disability Benefits Provisions, or under any
     disability insurance policy provided to Employee by Company as a fringe
     benefit.
                                    6 of 13
<PAGE>

     7.  Conflicts of Interest. During the Employment, the Employee will not
acquire, directly or indirectly, any financial interest in, accept gifts or
favors from, or establish any relationship other than on behalf of the Company
with, any customer, supplier, distributor, or other person who does or seeks to
do business with the Company, unless Employee has disclosed the financial
interest, gift, favor, or relationship to the Company's Board of Directors, in
writing, and has received the written approval of the Board of Directors for
such activity or transaction. The Employee is not otherwise precluded from
participating in the management of personal or family holdings, even though they
may offset the Company's operations.

     8.  Loyalty and Confidentiality; Company Property. The Employee will be
loyal to the Company during the Employment and will forever hold in strictest
confidence and will not use or disclose any information regarding the Company's
techniques, processes, developmental or experimental work, prospects, trade
secrets, customer or prospect names or information, or proprietary or
confidential information relating to the current or planned areas of activity,
prospects, areas of interest, services, sales, employees or business of the
Company, except as such disclosure or use may be required in connection with the
Employee's work for the Company. Upon termination of the Employment, the
Employee will deliver to the Company any and all materials relating to the
Company's business, including without limitation all customer lists and
information, keys, financial information, business notes, business plans,
Company provided autos or other equipment, credit cards, memoranda, prospects,
seismic information, specifications and documents, except as reasonably
necessary to ensure and verify the Company's compliance with this Agreement. All
Company property will be returned promptly and in good condition except for
normal wear. The Employee agrees not to retain any copies, reproductions or
summaries of any such materials. This covenant will continue in effect after
termination of the Employment and shall survive expiration of this Agreement.

     9.  Ideas, Concepts and Inventions Relating to Company's Business. All
business ideas and concepts and all inventions, improvements and developments
made or conceived by the Employee, either solely or in collaboration with
others, during the Employment, whether or not during working hours, and relating
to the Company's business or any aspect thereof, or to any business, product,
prospect, areas of activity or areas of interest the Company is considering
entering or developing, shall become and remain the exclusive property of the
Company, its successors and assigns. The Employee shall disclose promptly in
writing to the Company all such inventions, improvements and developments, and
will cooperate in confirming, protecting and obtaining legal protection of the
Company's ownership rights, and leasehold interest. This provision shall
continue in effect after termination of the Employment and shall survive
expiration of this Agreement as to ideas, concepts, inventions, improvements,
developments, and prospects made or conceived in whole or in part prior to the
date the Employment terminates.

     The Employee understands and agrees that the ideas, concepts, prospects,
production, areas of activity, areas of interest, inventions, improvements,
developments which the Employee invented, conceived or participated in prior to
becoming employed by the Company, and to which the Employee, or any assignee of
the Employee, now claims title, are available for development,

                                    7 of 13
<PAGE>

exploration, and can be capitalized upon, utilized by the Company for its own
gain. Any exceptions are completely described on an exhibit signed by the
parties and attached to this Agreement. If no such exhibit is attached, then
Employee represents and warrants that there are no such inventions,
improvements, developments or prospects to which the Company would be
restricted.

     10.  Covenant Not to Compete. During the Employment, and for one (1) year
after termination of the Employment, the Employee will not compete directly with
the Company. Competing directly with the Company shall be defined as purchasing
leases in an area defined by the Company as a Prospect for purposes of buying
leases, or divulging proprietary information about said area. It is expressly
understood and agreed that Employee shall in no way be restricted from acting as
a consultant or consulting in such areas as long as Employee does not use
proprietary information in such activity. Should the Company enter into
operations directly affecting the Employee's previously existing interests,
immediate family, relatives, or otherwise, the Employee will abstain from making
decisions or recommendations that materially adversely affect Company
operations. In the event that the Company should sell a working interest,
leasehold interest, any other such interest to the Employee, or his or her
immediate family, relatives, or otherwise, either corporately or individually,
the Employee will have the full rights and liberties associated to represent
said sale.

     11.  Entire Agreement. No agreements or representations, oral or otherwise,
express or implied, with respect to the Employee's Employment with the Company
or any of the subjects covered by this Agreement have been made by either party
which are not set forth expressly in this Agreement, and this Agreement
supersedes any pre-existing employment agreements and any other agreements on
the subjects covered by this Agreement. Other Company policies and practices not
addressed in this Agreement may be addressed in the Company's Employee Manual,
as may be modified from time to time.

     12.  Amendment and Waiver; Authority. No provisions of this Agreement may
be amended, modified, waived or discharged, and no additional obligations may be
imposed on the Company or the Employee, unless such waiver, modification,
discharge or obligation is (a) agreed to in a written agreement signed by an
officer of the Company authorized by the Board of Directors and the Employee and
(b) the terms of such written agreement are expressly approved by the Board of
Directors. No waiver by either party at any time of any breach or non-
performance of this Agreement by the other party shall be deemed a waiver of any
prior or subsequent breach or non-performance. No employee, officer or agent of
the Company other than the Board of Directors has any authority to offer
employment other than employment terminable at will by the Company, or to limit
the Company's right to terminate employment at will in any way.

     13.  Severability. The invalidity or unenforceability of any provision of
this Agreement will not affect the validity or enforceability of any other
provision of this Agreement, which will remain in full force and effect. If a
court of competent jurisdiction ever determines that any provision of this
Agreement (including but not limited to all or any part of the non-competition
covenant in Paragraph 10) is unenforceable as written, it is the intent of the
parties that such


                                    8 of 13
<PAGE>

provision shall be deemed narrowed or revised in such jurisdiction (as to
geographic scope, duration, or any other matter) to the extent necessary to
allow its enforcement.  Such revision shall thereafter govern in such
jurisdiction, subject only to any allowable appeals of such court decision.

     14.  Assignability. This Agreement contemplates personal services by the
Employee, and Employee may not transfer or assign Employee's rights or
obligations under this Agreement, except that Employee may designate
beneficiaries for Severance Pay in the event of Employee's death during the
Severance Pay Period, and may designate beneficiaries for benefits as allowed by
the Company's benefit programs. This Agreement may be assigned by the Company to
any subsidiary or parent corporation or a division of such corporation;
(however, the Company must obtain final approval by the Employee for such an
assignment of said Agreement, which will not be unreasonably withheld), or to
any entity which succeeds to all or substantially all of the Company's
businesses ("Successor Company").

     15.  Provisions Relating to Change in Control. For purposes of this
Agreement, the following definitions shall apply:

                     1.  Definition

     (a) "Change in Control" shall mean (i) the failure of the Continuing
     Directors at any time to constitute at least a majority of the members of
     the Corporation's Board of Directors; (ii) the acquisition by any Person
     (as defined in Section 13(d) and 14(d)(2) of the Securities Exchange Act of
     1934 (the "Act")) other than an Excluded Holder of beneficial ownership
     (within the meaning of Rule 13d-3 promulgated under the Act) of twenty
     percent (20%) or more of the outstanding Common Stock or the combined
     voting power of the Corporation's outstanding securities entitled to vote
     generally in the election of directors; (iii) the approval by the
     stockholders of the Corporation of a reorganization, merger or
     consolidation, unless with or into a Permitted Successor; or (iv) the
     approval by the stockholders of the Corporation of a complete liquidation
     or dissolution of the Corporation or the sale or disposition of all or
     substantially all of the assets of the Corporation other than to a
     Permitted Successor.

          (b) "Continuing Directors" mean the individuals constituting the
     Corporation's Board of Directors as of the date of this Agreement and any
     subsequent directors whose election or nomination for election by the
     Corporation's stockholders was approved by a vote of two-thirds (2/3) of
     the individuals who are then Continuing Directors, but specifically
     excluding any individual whose initial assumption of office occurs as a
     result of either an actual or threatened election contest (as the term is
     used in Rule 14a-11 of Regulation 14A promulgated under the Act) or other
     actual or threatened solicitation of proxies or consents by or on behalf of
     a Person other than the Corporation's Board of Directors.

          (c) "Excluded Holder" means the Corporation, a Subsidiary, any
     employee benefit plan (i.e., any plan or program established by the
     Corporation or a Subsidiary for the

                                    9 of 13

<PAGE>

     compensation or benefit of employees of the Corporation or any of its
     Subsidiaries) of the Corporation or a Subsidiary or any trust holding
     Common Stock or other securities pursuant to the terms of an employee
     benefit plan, or any member of the Miller Group.

          (d) "Miller Group" means (i) C.E. Miller, Kelly E. Miller, David A.
     Miller, Daniel R. Miller, Sue Ellen Bell and their respective spouses,
     lineal descendants and spouses of such descendants (collectively, the
     "Miller Family"), (ii) the estate of any member of the Miller Family, (iii)
     any trust established for the benefit of any member of the Miller Family,
     (iv) any trust of which the power to vote, dispose or direct the voting or
     disposition of any Common Stock of the Corporation included in the corpus
     of such trust is controlled by one or more members of the Miller Family,
     (v) without limiting the generality of the preceding clauses (iii) and
     (iv), the Kelly E. Miller Retained Annuity Trust #1, the David A. Miller
     Retained Annuity Trust #1, the Daniel R. Miller Retained Annuity Trust #1,
     the Sue Ellen Bell Retained Annuity Trust #1, the Kelly E. Miller Trust,
     the David A. Miller Trust, the Daniel R. Miller Trust and the Sue E. Bell
     Trust, (vi) any corporation of which a majority of the outstanding shares
     of capital stock entitled to vote generally for directors is beneficially
     owned by, or a partnership of which a majority of the partnership interests
     with voting rights are beneficially owned by, or a limited liability
     company of which a majority of the membership interests with voting rights
     are beneficially owned by, any of the individuals or entities identified in
     clauses (i) through (v) above, including without limitation Eagle
     Investments, Inc., Eagle International, Inc., Oak Shores Investments, Inc.,
     Double Diamond Enterprises, Inc., and Frontier Investments, Inc.

          (e) "Permitted Successor" means a corporation which, immediately
     following the consummation of a transaction specified in clauses (iii) and
     (iv) of the definition of "Change in Control" above, satisfies each of the
     following criteria:  (A) sixty percent (60%) or more of the outstanding
     common stock of the corporation and the combined voting power of the
     outstanding securities of the corporation entitled to vote generally in the
     election of directors (in each case determined immediately following the
     consummation of the applicable transaction) is beneficially owned, directly
     or indirectly, by all or substantially all of the Persons who were the
     beneficial owners of the Corporation's outstanding Common Stock and
     outstanding securities entitled to vote generally in the election of
     directors (respectively) immediately prior to the applicable transaction,
     (B) no Person other than an Excluded Holder beneficially owns, directly or
     indirectly, twenty percent (20%) or more of the outstanding common stock of
     the corporation or the combined voting power of the outstanding securities
     of the corporation entitled to vote generally in the election of directors
     (for these purposes the term Excluded Holder shall include the corporation,
     any Subsidiary of the corporation and any employee benefit plan of the
     corporation or any such Subsidiary or any trust holding common stock or
     other securities of the corporation pursuant to the terms of any such
     employee benefit plan), and (C) at least a majority of the Board of
     Directors is comprised of Continuing Directors.

                                   10 of 13
<PAGE>

          (f) "Person" means any individual, corporation (including any non-
     profit corporation), general or limited partnership, limited liability
     company, joint venture, estate, trust, association, organization or other
     entity or governmental body.

          (g) "Subsidiary" means any corporation or other entity of which fifty
     percent (50%) or more of the outstanding voting stock or voting ownership
     interest is directly or indirectly owned or controlled by the Corporation
     or by one or more Subsidiaries of the Corporation.

               2.   Effect of Change in Control

          If there is a Change in Control of the Company, or the Employee
     terminates the employment for Good Reason as permitted under Paragraph
     5(d), then the Employee shall receive the Lump Sum Payment described in the
     Severance Pay provided under Paragraph 6, and in addition all unvested
     stock options and restricted stock described in Paragraphs 4(b) and 4(c)
     above will vest immediately.


               3.   Special Tax Provision

          If any payment or payments to be made to the Employee by the Company
     following the termination of the Employee's employment, whether such
     payments are to be made under this Agreement or otherwise, would result in
     Employee incurring any excess parachute payment excise tax under IRC
     Sections 280G and 4999, then those payments that are to be made to
     Employee under this Agreement and that constitute "parachute payments" (as
     that term is defined under IRC Section 280G) shall be reduced or delayed to
     the extent necessary to eliminate any "excess parachute payments" (as that
     term is defined under IRC Section 280G) to Employee; provided, however,
     that  such reductions or delays shall be made if, and only if (A), below,
     is greater than (B), below, where: (A) equals  the present value as of the
     date of termination of Employee's employment of the total payments to be
     made to the Employee after such reductions or delays; and (B) equals the
     present value as of the date of termination of the Employee's employment of
     the  total payments to be made to  the Employee in the absence of such
     reduction and after application of the 20% excise tax on excess parachute
     payments. If such reductions or delays are to be made, the Employee shall
     determine which payments shall be reduced or delayed. Employee's
     determination as to whether reductions or delays are called for under this
     Paragraph shall be final and binding, if reasonable. If the Company  fails
     to accept any reasonable determination of Employee under this Paragraph,
     the Company shall reimburse Employee for all expenses and losses (including
     but not limited to attorney fees and any  additional taxes or interest or
     penalties on unpaid taxes) incurred by Employee as a result of the
     Company's failure to accept such determinations.

                                   11 of 13
<PAGE>

     16.  Notices.  Notices to a party under this Agreement must be
personally delivered First Class mail, Facsimile, or sent by certified mail
(return receipt requested) and will be deemed given upon post office delivery or
attempted delivery to the recipient's last known address. Notices to the Company
must be sent to the attention of the Company's Board of Directors.

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

     18.  Arbitration. The Company and the Employee agree that the sole and
exclusive method for resolving any dispute between them regarding this Agreement
or its interpretation application or its termination shall be arbitration under
the procedures set forth in this Paragraph; provided, however, that nothing in
this Paragraph prohibits a party from seeking preliminary or permanent
injunctive relief from a court of competent jurisdiction, or from seeking
judicial enforcement of the arbitration award. If either party demands
arbitration of a dispute covered by this Paragraph, an arbitrator shall be
selected, and the arbitrator shall hold a hearing at which both parties may
appear, with or without counsel, and present evidence and argument. Pre-hearing
discovery shall be allowed in the discretion of and to the extent deemed
appropriate by the arbitrator, and the arbitrator shall have subpoena power. The
procedural rules for an arbitration hearing under this Paragraph, and the
selection of the arbitrator shall be pursuant to the rules of the American
Arbitration Association for Commercial Arbitration Hearings and such rules as
the arbitrator may determine. The hearing shall be held in Houston, Texas. The
award of the arbitrator(s) shall be final and binding and may be enforced by and
certified as a judgment of any court of competent jurisdiction. The fees and
expenses of the arbitrator shall be paid equally by the Company and the
Employee. The attorney fees and expenses incurred by the parties shall be paid
by the losing party.

     19.  Governing Law. The validity, interpretation, and construction of
this Agreement are to be governed by the laws of the State of Texas, without
regard to principles of conflicts of law.

                                   12 of 13


                     *     *     *     *     *     *     *
<PAGE>

     The parties have signed this Agreement as of the date and year first
above written.


                                         /s/ Lew P. Murray
                                        --------------------------------------
                                        Lew P. Murray
                                                                   "Employee"


                                        MILLER EXPLORATION COMPANY



                                        By  /s/ Kelly E. Miller
                                          ------------------------------------

                                        Its    President
                                           -----------------------------------

                                                                   "Company"



                                   13 of 13