<PAGE>

                                                                   EXHIBIT 10.19

                             EMPLOYMENT AGREEMENT
                             --------------------

     THIS EMPLOYMENT AGREEMENT (this "Agreement") is made between Titan
Resources Holdings, Inc., a Delaware corporation (the "Company"), and Jack D.
Hightower ("Executive");

                             W I T N E S S E T H:
                             - - - - - - - - - -

     WHEREAS, pursuant to the terms and conditions of that certain Agreement and
Plan of Merger (the "Merger Agreement"), dated December 13, 1999, among Union
Oil Company of California, a California corporation ("Union Oil"), the Company,
TRH, Inc., a Delaware corporation ("TRH"), and Titan Exploration, Inc., a
Delaware corporation ("Titan"), TRH will be merged with and into Titan, which
will be the surviving corporation and become a wholly-owned subsidiary of the
Company; and

     WHEREAS, Executive is the Chairman of the Board, Chief Executive Officer
and President of Titan; and

     WHEREAS, the Board of Directors of the Company (the "Board") has determined
that it is in the best interests of the Company and its stockholders to assure
that the Company will have the continued dedication of Executive,
notwithstanding the consummation of the transactions contemplated by the Merger
Agreement or the possibility, threat or occurrence of a Change of Control (as
defined below) of the Company; and

     WHEREAS, the Board believes it is imperative to diminish the inevitable
distraction of Executive by virtue of the personal uncertainties and risks
created by a pending or threatened Change of Control and to encourage
Executive's full attention and dedication to the Company in the event of any
pending or threatened Change of Control, and to provide Executive with
compensation and benefits upon a Change of Control which ensure that the
compensation and benefits expectations of Executive will be satisfied and which
are competitive with those of other corporations; and

     WHEREAS, in order to accomplish these objectives, the Board has caused the
Company to enter into this Agreement;

     NOW, THEREFORE, in consideration of the mutual promises contained herein,
the parties, intending to be legally bound, agree as follows:

     1.   Effective Date.  This Agreement shall become effective as of the date
          --------------
on which the transactions contemplated by the Merger Agreement are consummated
(the "Effective Date") and shall terminate and be of no force or effect if the
Merger Agreement is terminated in accordance with its terms.

     2.   Employment and Duties. Executive shall have such duties, functions,
          ---------------------
responsibilities, and authority customarily appertaining to the position of
President, Chief Executive Officer and Chairman of the Board in a corporation;
subject, however, to the directives of the Board of Directors
<PAGE>

of the Company. Executive shall devote his full time, skill, and attention and
his best efforts during normal business hours to the business and affairs of the
Company, and in furtherance of the business and affairs of the Company and its
subsidiaries; except for usual, ordinary, and customary periods of vacation and
absence due to illness or other disability; provided, however, that Executive
may devote reasonable periods of time in connection with the following
activities, if such activities do not materially interfere with the performance
of Executive's duties and services hereunder and do not consume more than 10% of
Executive's working hours (which for purposes hereof will generally constitute a
40 hour work week):

     (a)  serving as a director or a member of a committee of any organization,
if serving in such capacity does not involve any conflict with the business of
the Company and its subsidiaries and such organization is not in competition in
any manner whatsoever with the business of the Company and its subsidiaries (it
being acknowledged by the parties that Employee's service as an advisory
director of Chase Bank, Midland, Texas is permissible hereunder);

     (b)  fulfilling speaking engagements;

     (c)  engaging in charitable and community activities; and

     (d)  managing his personal investments.

     3.   Base Compensation.
          -----------------

     (a)  Salary.  The Company shall pay Executive for his services under this
          ------
Agreement a base annual salary as may be determined by the Board of Directors
from time to time, provided that such salary shall not be less than $480,000
(before federal and state withholdings).  The base salary shall be payable semi-
monthly or in such other installments as shall be consistent with the Company's
general payroll practices.

     (b)  Bonus.  In addition to his annual base salary, Executive shall be
          -----
entitled to an annual cash bonus in an amount, as may be determined by the Board
of Directors from time to time, provided that such cash bonus shall not be less
than $240,000.

     4.   Fringe Benefits.  During the term hereof, Executive shall be entitled
          ---------------
to participate in any benefit programs and incentive plans applicable to all
employees or to executive employees of the Company on the same basis as such
benefits and plans are customarily made available by the Company from time to
time, including without limitation all employee retirement, insurance, vacation,
sick leave, long-term disability and other benefit programs, and grants of
rights or options to acquire equity interests or other awards provided for under
the Company's incentive plans, as such benefits and plans may be modified,
amended or terminated from time to time.

     5.   Professional Organization Dues.  The Company shall pay the initiation
          ------------------------------
fees and periodic dues for membership in any oil and gas professional
organizations including the National Petroleum Council in which Executive is
currently a member, or which are otherwise approved by

                                       2
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the Board of Directors of the Company, and the Company shall pay all charges and
expenses, including reasonable travel expenses, incurred by Executive in
connection with membership in such organizations.

     6.   Vacations.  Executive shall be entitled to take such vacations as he
          ---------
may desire, with pay, provided that such vacations do not interfere with the
performance of his duties and services hereunder.

     7.   Business Expenses.  Executive shall be reimbursed by the Company for
          -----------------
expenses reasonably paid or incurred by him in connection with the performance
of his duties hereunder upon presentation of expense statements, receipts or
vouchers or such other supporting information reasonably evidencing such
expenses.

     8.   Term.  The term of Executive's employment by the Company hereunder
          ----
shall initially be for a period of three (3) years commencing on the Effective
Date of this Agreement. Beginning on the first anniversary of the Effective Date
of this Agreement, and on each subsequent anniversary thereof (each such
anniversary being referred to as an "Extension Date"), the term of this
Agreement shall be extended for an additional one year period, unless either
party provides written notice to the other prior to an Extension Date that the
term of this Agreement shall not be extended. It is the express intent of both
parties to this Agreement that the provisions of this Section 8 are intended to
ensure that upon notice of an election not to extend the term of this Agreement,
the remaining term of this Agreement will at all times be not less than three
(3) years.

     9.   Termination.  Executive's employment with the Company shall terminate
          -----------
upon the first to occur of the (i) expiration of the term of this Agreement (as
extended pursuant to Section 9 hereof), (ii) death of Executive, (iii)
disability of Executive, but only upon compliance with the provisions of Section
11 hereof, (iv) termination of Executive for Cause (as defined in Section 12),
(v) termination by Executive pursuant to Section 13 hereof, or (vi) written
consent of all parties to this Agreement.

     10.  Death of Executive.  The employment of Executive hereunder shall cease
          ------------------
on the date of his death. The Company will purchase life insurance on the life
of Executive in an amount not less than $3,000,000, the benefits of which will
be payable one-half to Executive's beneficiary and one-half to the Company.
Executive's "beneficiary" is the person or persons (who may be designated
concurrently, successively or contingently) designated by Executive in his last
effective writing filed with the Company prior to his death, or if Executive
shall have failed to make an effective designation, Executive's beneficiary is
his spouse, if Executive is married and his spouse is living at the time of each
payment, and otherwise his surviving children. Executive shall assist the
Company in procuring such insurance by submitting to such examinations and by
signing such applications and other instruments as may be reasonable and as may
be required by the insurance carriers to which application is made for any such
insurance. Executive represents that, to the best of his knowledge, he is
currently insurable at standard premium rates for life insurance policies.

                                       3
<PAGE>

     11.  Disability of Executive.  If, as a result of Executive's incapacity
          -----------------------
due to physical or mental illness, Executive shall have been absent from his
duties hereunder on a full-time basis for the entire period of six consecutive
months, and within thirty (30) days after written notice of termination is given
(which may occur before or after the end of such six-month period) shall not
have returned to the performance of his duties hereunder on a full-time basis (a
"Disability"), employment of Executive hereunder shall cease.

     The Company shall purchase disability insurance to cover such a contingency
with coverage and benefits mutually agreeable to the Company and Executive.
Executive shall assist the Company in procuring such insurance by submitting to
such examinations and by signing such applications and other instruments as may
be reasonable and as may be required by the insurance carriers to which
application is made for any such insurance. Executive represents that, to the
best of his knowledge, he is currently insurable at standard premium rates for
disability insurance policies. During any period prior to termination during
which Executive fails to perform his duties hereunder as a result of incapacity
due to physical or mental illness ("disability period"), Executive shall
continue to receive his full salary at the rate then in effect for such period
until his employment terminates pursuant to this Section 11.

     If employment of Executive hereunder terminates because of Executive's
incapacity, Executive (or, in the event of his legal incapacity, a court-
appointed guardian for his benefit) shall receive those benefits payable under
the disability policy or policies (purchased in compliance with the foregoing
provisions) in effect at such time.

     12.  Termination for Cause.  The Company may terminate Executive's
          ---------------------
employment hereunder for Cause. For purposes of this Agreement, the Company
shall have "Cause" to terminate Executive's employment hereunder upon (A)
Executive's conviction of, or plea of nolo contendere to, any felony of theft,
fraud, embezzlement or violent crime; (B) the willful and continued failure by
Executive to substantially perform Executive's duties with the Company (other
than such failure resulting from Executive's incapacity due to physical or
mental illness), after a written demand for substantial performance is delivered
to Executive by the Board, which specifically identifies the manner in which the
Board believes that Executive has not substantially performed Executive's duties
or (C) the willful engaging by Executive in misconduct which is materially
injurious to the interests of the Company or any successor thereto (or any
affiliate of the Company or a successor thereto).  For purposes of this Section
12, no act, or failure to act, on Executive's part shall be considered "willful"
unless done, or omitted to be done, by Executive not in good faith and without
reasonable belief that Executive's action or omission was in the best interest
of the Company. Notwithstanding the foregoing, Executive shall not be deemed to
have been terminated for Cause unless and until there shall have been delivered
to Executive a copy of a notice of termination from the Board, after (x)
reasonable notice to Executive, (y) an opportunity for Executive, together with
Executive's counsel (the reasonable fees of which the Company shall pay promptly
as incurred), to be heard before the Board, finding that, in the good faith
opinion of the Board, Executive was guilty of conduct set forth above in clauses
(A), (B) or (C) of the second sentence of this Section 12 and specifying the
particulars thereof in detail, and (z) in the case of conduct set forth in
clause (B), a period of not less than sixty (60) days to remedy same.

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<PAGE>

     13.  Termination by Executive.  Executive may terminate his employment
          ------------------------
hereunder (i) for Good Reason, or (ii) for any other reason upon providing at
least 30 days advance written notice.

     For purposes of this Agreement, "Good Reason" shall mean any of the
following (without Executive's express written consent):

     (a)  A failure by the Company to comply with any material provision of this
Agreement which has not been cured within sixty (60) working days after notice
of such noncompliance has been given by Executive to the Company;

     (b)  A material change in the nature or scope of Executive's duties from
those engaged in by Executive immediately prior to the date of this Agreement;

     (c)  A reduction in Executive's annual base compensation from that provided
to him pursuant to this Agreement;

     (d)  A material diminution in Executive's eligibility to participate in or
in the benefits provided to Executive under any bonus, stock option or other
incentive compensation plans or employee welfare and pension benefit plans
(including medical, dental, life insurance, retirement and long-term disability
plans) from that provided to him on the date of this Agreement;

     (e)  Any required relocation of Executive outside of Texas (including any
required business travel in excess of the greater of 90 days per year or the
level of business travel of Executive for the year prior to the date of this
Agreement);

     (f)  Executive and the Company, or any successor thereto, shall fail to
reach an agreement on or prior to the date of closing of a transaction that
constitutes a Change of Control as to the terms of Executive's employment
following such Change of Control, which terms are acceptable to Executive in his
sole discretion; or

     (g)  Union Oil, together with all "affiliates" and "associates" (as such
terms are defined in Rule 12b-2 under the Securities Exchange Act of 1934, as
amended (the "Exchange Act")) of such person (as well as any "Person" or "group"
as those terms are used in Sections 13(d) and 14(d) of the Exchange Act), shall
become the "beneficial owner" or "beneficial owners" (as defined in Rules 13d-3
and 13d-5 under the Exchange Act), directly or indirectly, of securities of the
Company representing in the aggregate 85% or more of either the then outstanding
shares of common stock of the Company or the Voting Securities of the Company.

     An election by Executive to terminate for Good Reason shall not be deemed a
voluntary termination of employment by Executive for the purpose of this
Agreement or any plan or practice of the Company.

     14.  Notice of Termination.  Any termination of Executive's employment by
          ---------------------
the Company or by Executive pursuant to Sections 11, 12 or 13 shall be
communicated by written Notice of

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<PAGE>

Termination to the other party hereto. For purposes of this Agreement, a "Notice
of Termination" shall mean a notice which shall indicate the specific
termination provisions in this Agreement relied upon and shall set forth in
reasonable detail the facts and circumstances claimed or provide a basis for
termination of Executive's employment under the provision so indicated.

     15.  Termination of Employment for Cause or Without Good Reason.
          ----------------------------------------------------------

     (a)  If the Company shall terminate Executive's employment for Cause, then
upon such termination all rights, benefits and compensation of Executive under
this Agreement shall immediately terminate, except that equity options, if any,
shall continue to be governed in accordance with their terms.  The rights and
remedies of the Company as set forth in this Section 15(a) shall be cumulative
with and shall be in addition to (i) any and all other relief available to the
Company for breach by Executive of any other provision of this Agreement, and
(ii) any and all other general or equitable relief to which the Company may be
entitled by reason of such breach.

     (b)  If Executive shall voluntarily terminate his employment other than for
Good Reason, then (i) within 30 days following such termination, the Company
shall pay to Executive a sum equal to (A) the amount of Executive's annual base
salary, plus (B) an amount equal to the average annual bonus received by
Executive pursuant to Section 3(b) hereof during the immediately preceding three
(3) years (but in no event less than $240,000), (ii) Executive shall be entitled
to continue to participate in all benefit programs and incentive plans as
provided in Section 4 of this Agreement during a period equal to the remainder
of Executive's employment term hereunder, and (iii) all restricted stock,
options or other rights with respect to equity interests in the Company and/or
its affiliates granted to Executive on or before such date of termination shall
continue to be governed in accordance with their terms.

     16.  Other Termination of Employment.  If Executive shall terminate his
          -------------------------------
employment for Good Reason under Section 13 hereof or other than for death under
Section 10, disability under Section 11 or pursuant to Section 15, then (i)
within 30 days following such termination, upon Executive's execution of the
General Release, the Company shall pay to Executive an amount equal to three (3)
times the sum of (A) the amount of Executive's annual base salary, plus (B) an
amount equal to the average annual bonus received by Executive pursuant to
Section 3(b) hereof during the immediately preceding three (3) years (but in no
event less than $240,000), (ii) Executive shall be entitled to continue to
participate in all benefit programs and incentive plans as provided in Section 4
of this Agreement during a period equal to the remainder of Executive's
employment term hereunder, (iii) all restricted stock, options or other rights
with respect to equity interests in the Company and/or its affiliates granted to
Executive on or before such date of termination shall immediately vest as of the
date of such termination, and (iv) the Company or any successor thereto (or an
affiliate of the Company or any successor thereto) shall take all such action as
may be necessary or appropriate to amend any option to purchase the Company's
common stock held by Executive to provide that such option will not terminate as
a result of or in connection with Executive's termination of employment with the
Company or any successor thereto (or an affiliate of the Company or any
successor thereto), but may continue to be exercised following such termination
of employment until the date on which such options otherwise would terminate or

                                       6
<PAGE>

expire; provided that, the Company shall also pay to Executive those amounts
provided in Sections 10 and 11 pursuant to the terms thereof.

     17.  Change of Control.  For purposes of this Agreement, a "Change of
          -----------------
Control" shall be deemed to have occurred if a Company Change of Control or a
Unocal Change of Control (each as defined in Section 18) occurs.

     18.  Put Right.
          ---------

     (a)  Upon the occurrence of a Put Event, Executive shall have the option
(the "Put Option"), exercisable at any time before the 90th day after the Put
Event, to sell to the Company all or part (in each case, subject to Section
18(e)) of his Continuing Company Shares at a price calculated in accordance with
the provisions of Section 18(d); provided, however, that if Executive fails to
exercise such Put Option (other than with respect to a Put Event described in
clause (C) of the definition of Put Event) or exercises such Put Option for less
than all of his Continuing Company Shares, Executive shall not have the right to
require the Company to purchase any shares upon the occurrence of any future Put
Event. If Executive exercises the Put Option within the specified period by
giving notice (the "Put Notice") to the Company of his or her election to do so
(the date such notice is given is the "Put Date"), the Company shall be required
to purchase all (but, subject to Section 18(e), not less than all) of the
Continuing Company Shares specified by Executive in the Put Notice, such
purchase to be effected in the manner, upon the terms and for the consideration
set forth hereafter.

     (b)  The consummation of any purchase required under this Section 18 shall
be held at a "Put Closing", and the time and date upon which the Put Closing
shall take place shall constitute the "Put Closing Date". The Put Closing shall
be held at the principal office of the Company on the date designated by
Executive in the Put Notice or on such other date as shall be mutually agreed
upon in writing by the Company and Executive; provided, however, that the Put
Closing Date shall not be more than 30 days (or a period of such additional
length as reasonably necessary to complete the additional valuations
contemplated in the definition of Net Asset Value) nor less than three days
after the delivery of the Put Notice. In addition to providing the Put Closing
Date, the Put Notice shall set forth the number of shares to be purchased by the
Company and the Purchase Price (as defined below).

     (c)  At the Put Closing, Executive shall present to the Company all share
certificates or option agreements for Continuing Company Shares required to be
purchased, duly endorsed in blank and in proper form for transfer, or with
separate stock powers attached, duly endorsed in blank and in proper form for
transfer, free and clear of any encumbrances. At the Put Closing, the Company,
upon receipt of a conforming tender from Executive, shall tender full payment of
the Purchase Price in immediately available funds by confirmed wire transfer to
a bank account to be designated by Executive (such designation to occur no later
than the second business day prior to the Put Closing Date).

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<PAGE>

     (d)  The total purchase price (the "Purchase Price") for all the shares of
Common Stock to be purchased pursuant to this Section 18 shall be equal to the
number of shares of Continuing Company Shares held by, or issuable to, Executive
which are subject to the Put Closing multiplied by the Price Per Share.  The
"Price Per Share" shall be equal to the Net Asset Value divided by the Fully-
Diluted Outstanding Share Amount, each determined as of the Put Date.

     (e)  If the Company is unable to consummate any desired purchase of
Continuing Company Shares pursuant to the terms of this Agreement because of
limitations contained in the Delaware Business Corporation Act (or a successor
statute thereof) or other applicable law, the Company agrees to use its best
efforts to take all such action as may be available to place the Company in a
position to carry out any required purchase under this Agreement. If the
Company, after the taking of any action by it as contemplated in the immediately
preceding sentence, is unable to consummate the purchase of all the shares of
Executive's Continuing Company Shares as required, the Company shall purchase at
the applicable price all shares of Continuing Company Shares that the Company
shall then be authorized to purchase under the provisions of applicable law, and
shall purchase the remainder of such shares as soon thereafter as possible at
the applicable price, plus accrued interest on such purchase price at the
floating prime borrowing rate specified by the lead bank on the Company's
principal revolving credit facility or, if there is no such bank, a comparable
prime rate selected in good faith by the Board of Directors.

     (f)  Each of the following terms has the meaning set forth below:

          (i)  "Common Stock" means the common stock, par value $.01 per share,
     of the Company.

          (ii) A "Company Change of Control" shall be deemed to have occurred
     for purposes of this Agreement if:

               (A)  individuals who, as of the date hereof, constitute the Board
          of Directors of the Company (the "Company Incumbent Board") cease for
          any reason to constitute at least 40% of such Board of Directors,
          provided that any person becoming a director subsequent to the date
          hereof whose election, or nomination for election by the stockholders
          of the Company was approved by a vote of at least a majority of the
          directors then comprising the Company Incumbent Board shall be, for
          purposes of this Agreement, considered as though such person were a
          member of the Company Incumbent Board;

               (B)  the stockholders of the Company approve a reorganization,
          merger or consolidation, in each case, with respect to which persons
          who were the stockholders of the Company immediately prior to such
          reorganization, merger or consolidation do not, immediately
          thereafter, own voting securities representing more than 40% of the
          Voting Securities of the reorganized, merged or consolidated company;

                                       8
<PAGE>

                (C)  the Company sells, leases or exchanges or agrees to sell,
          lease or exchange all or substantially all of its assets to any other
          person or entity;

                (D)  the Company adopts a plan of dissolution or liquidation; or

                (E)  any "person," as that term is defined in Section 3(a)(9) of
          the Exchange Act (other than Union Oil or any affiliate thereof and
          other than the Company, any of its subsidiaries, any employee benefit
          plan of the Company or any of its subsidiaries, or any entity
          organized, appointed or established by the Company for or pursuant to
          the terms of such a plan), together with all "affiliates" and
          "associates" (as such terms are defined in Rule 12b-2 under the
          Exchange Act) of such person (as well as any "Person" or "group" as
          those terms are used in Sections 13(d) and 14(d) of the Exchange Act),
          shall become the "beneficial owner" or "beneficial owners" (as defined
          in Rules 13d-3 and 13d-5 under the Exchange Act), directly or
          indirectly, of securities of the Company representing in the aggregate
          40% or more of either the then outstanding shares of Common Stock or
          the Voting Securities of the Company.

          (iii) "Continuing Company Shares" means 1,888,582 shares of Common
     Stock, being the shares resulting from the conversion in TRH, Inc.'s merger
     with Titan pursuant to the Merger Agreement of shares of Titan common stock
     owned by Executive as of December 1, 1999, plus any shares of Common Stock
     acquired by Executive pursuant to the exercise of any stock options
     previously or hereafter granted to Executive pursuant to any stock option
     or similar stock incentive plan of the Company.

          (iv)  "Fully-Diluted Outstanding Share Amount" means that number of
     shares of Common Stock that would be issued and outstanding after taking
     into account the conversion or exchange of all issued and outstanding
     securities of the Company or any of its affiliates which are convertible or
     exchangeable into Common Stock.

          (v)   "Net Asset Value" means (A) 110% of the following amount: (1)
     the net equity ownership in the proved reserves of the Company, calculated
     using the average of the three-year strip price for the 120 days prior to
     the Put Date (NYMEX less applicable differentials) at a 10% discount rate
     and reflecting any increase or decrease resulting from hedges in place,
     plus (2) the proved reserves not included within the terms of the preceding
     clause (1), calculated as in clause (1), attributable to the Company's net
     equity interest in any corporation, partnership, limited liability company
     or other entity (including the Company's net equity interest in proved
     reserves resulting from any promoted interest, back-in after payout or
     other carried or increasing interest in such entities) as of the Put Date;
     less (B) the funded debt, including bank debt and senior and subordinated
     debt securities issued pursuant to indentures of the Company, as of the Put
     Date; and less (C) such funded debt attributable to the Company's net
     equity interest in each corporation, partnership, limited liability company
     or other entity referred to in clause (A)(1), as of the Put Date. In no
     event shall "Net Asset Value" include the value of public securities,
     purchased by the Company in the

                                       9
<PAGE>

     open market, of issuers in which the Company has no control or board
     representation. For purposes of valuing the proved reserves of the Company,
     such proved reserves shall be determined at the sole discretion of the
     Board of Directors (the"First Valuation"); provided, however, that, if the
     First Valuation is not acceptable to Executive, he may request a second
     valuation to be performed at his cost by a third party, independent
     engineering firm (the "Second Valuation"); provided further, if the Second
     Valuation is not acceptable to the Company, the Executive and the Company
     shall select another third party firm to perform a final valuation (the
     "Final Valuation") and the cost of the Final Valuation shall be shared
     equally by the Company and the Executive. If the Final Valuation exceeds
     the Second Valuation, the Second Valuation shall be used in determining Net
     Asset Value. If the First Valuation exceeds the Final Valuation, the First
     Valuation shall be used in determining Net Asset Value. If the Final
     Valuation is between the First Valuation and the Second Valuation, an
     average of all three shall be used in determining Net Asset Value.

          (vi)   "Put Event" means any of the following:

                 (A) termination of Executive's employment by the Company
          without Cause (as defined in Section 12);

                 (B) termination of Executive's employment for any reason on or
     after the third anniversary of the date of this Agreement;

                 (C) occurrence of a Company Change of Control or a Unocal
     Change of Control;

                 (D) the death or Disability (as defined in Section 11) of
          Executive;

                 (E) the termination by Executive of his employment with the
          Company for Good Reason (as defined in Section 13); or

                 (F) Union Oil, together with all "affiliates" and "associates"
          (as such terms are defined in Rule 12b-2 under the Exchange Act) of
          such person (as well as any "Person" or "group" as those terms are
          used in Sections 13(d) and 14(d) of the Exchange Act), shall become
          the "beneficial owner" or "beneficial owners" (as defined in Rules
          13d-3 and 13d-5 under the Exchange Act), directly or indirectly, of
          securities of the Company representing in the aggregate 85% or more of
          either the then outstanding shares of common stock of the Company or
          the Voting Securities of the Company.

          (vii)  "Unocal" means Unocal Corporation, a Delaware Corporation.

          (viii) A "Unocal Change of Control" shall be deemed to have occurred
     for purposes of this Agreement if:

                                       10
<PAGE>

                (A) individuals who, as of the date hereof, constitute the Board
          of Directors of Unocal (the "Unocal Incumbent Board") cease for any
          reason to constitute at least 50% of such Board of Directors, provided
          that any person becoming a director subsequent to the date hereof
          whose election, or nomination for election by the stockholders of
          Unocal was approved by a vote of at least a majority of the directors
          then comprising Unocal Incumbent Board shall be, for purposes of this
          Agreement, considered as though such person were a member of Unocal
          Incumbent Board;

                (B) the stockholders of Unocal approve a reorganization, merger
          or consolidation, in each case, with respect to which persons who were
          the stockholders of Unocal immediately prior to such reorganization,
          merger or consolidation do not, immediately thereafter, own voting
          securities representing more than 50% of the Voting Securities of the
          reorganized, merged or consolidated company;

                (C) Unocal sells, leases or exchanges or agrees to sell, lease
          or exchange all or substantially all of its assets to any other person
          or entity;

                (D) Unocal adopts a plan of liquidation or dissolution; or

                (E) any "person," as that term is defined in Section 3(a)(9) of
          the Exchange Act (other than Unocal, any of its subsidiaries, any
          employee benefit plan of Unocal or any of its subsidiaries, or any
          entity organized, appointed or established by Unocal for or pursuant
          to the terms of such a plan), together with all "affiliates" and
          "associates" (as such terms are defined in Rule 12b-2 under the
          Exchange Act) of such person (as well as any "Person" or "group" as
          those terms are used in Sections 13(d) and 14(d) of the Exchange Act),
          shall become the "beneficial owner" or "beneficial owners" (as defined
          in Rules 13d-3 and 13d-5 under the Exchange Act), directly or
          indirectly, of securities of Unocal representing in the aggregate 50%
          or more of either the then outstanding shares of common stock of
          Unocal or the Voting Securities of Unocal.

          (ix)  "Voting Securities" means the combined voting power entitled to
     vote generally in the election of directors.

     19.  Legal Fees.  The Company shall pay all reasonable legal fees and
          ----------
expenses promptly as they are incurred by Executive in seeking to obtain or
enforce any right or benefit provided by this Agreement.

     20.  Gross-Up Payment.  Notwithstanding any provision in this Agreement to
          ----------------
the contrary, if it shall be determined that any payment, distribution or
transfer of property or rights thereto by the Company or any successor thereto
to or for the benefit of Executive (whether paid, payable, distributed,
distributable, transferred or transferable pursuant to the terms of this
Agreement or otherwise, including but not limited to the acceleration of vesting
of stock options), but determined

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<PAGE>

without regard to any additional payments required pursuant to this Section 20
(a "Payment") would be subject to the excise tax imposed by Section 4999 of the
Internal Revenue Code of 1986, as amended (the "Code"), or any interest or
penalties are incurred by Executive with respect to such excise tax (such excise
tax, together with any such interest and penalties, hereinafter collectively
referred to as the "Excise Tax"), then the Executive shall be entitled to
receive an additional payment from the Company or its successor (a "Gross-Up
Payment") in an amount such that after payment by Executive of all taxes
(including any interest or penalties imposed with respect to such taxes),
including, without limitation, any income taxes (and any interest and penalties
imposed with respect thereto) and Excise Tax imposed upon the Gross-Up Payment,
Executive retains an amount of Gross-Up Payment equal to the Excise Tax imposed
upon the Payments.

     21.  Confidentiality; Non-Compete.  During the time of Executive's
          ----------------------------
employment and for a period of one (1) year following the termination of
Executive's employment with the Company, Executive agrees not to compete with
the Company for any acquisition, prospect or project that the Company was
pursuing prior to Executive's termination, and Executive shall hold in strict
confidence and shall not, directly or indirectly, disclose or reveal to any
person, or use for his own personal benefit or for the benefit of anyone else,
any trade secrets, confidential dealings, or other confidential or proprietary
information of any kind, nature, or description (whether or not acquired,
learned, obtained, or developed by Executive alone or in conjunction with
others) belonging to or concerning the Company or any of its subsidiaries,
except (i) with the prior written consent of the Company duly authorized by its
Board of Directors, (ii) in the course of the proper performance of Executive's
duties hereunder, (iii) for information (x) that becomes generally available to
the public other than as a result of unauthorized disclosure by Executive or his
affiliates or (y) that becomes available to Executive on a nonconfidential basis
from a source other than the Company or its subsidiaries who is not bound by a
duty of confidentiality, or other contractual, legal, or fiduciary obligation,
to the Company, or (iv) as required by applicable law or legal process.

     22.  Miscellaneous.  (a)  Notices.  Any notice or communication required or
          -------------        -------
permitted hereunder shall be given in writing and shall be (i) sent by first
class registered or certified United States mail, postage prepaid, (ii) sent by
overnight or express mail or expedited delivery service, (iii) delivered by hand
or (iv) transmitted by facsimile transmission, to the address or fax number for
the party as set forth opposite such party's name on the signature page hereof,
or to such other address or to the attention of such other person as hereafter
shall be designated in writing by the applicable party in accordance herewith.
Any such notice or communication shall be deemed to have been given as of the
date of first attempted delivery at the address or fax number and in the manner
provided above.

     (b)  Successors and Assigns.  This Agreement is personal in nature and
          ----------------------
neither of the parties hereto shall, without the consent of the other, assign or
transfer this Agreement or any rights or obligations hereunder; provided,
however, that in the event of a merger, consolidation or transfer or sale of all
or substantially all of the assets of the Company, this Agreement shall be
binding upon the successor to the Company's business and assets.

                                       12
<PAGE>

     (c)  Interpretation.  When the context in which words are used in this
          --------------
Agreement indicates that such is the intent, words in the singular number shall
include the plural and vice versa, and the words in masculine gender shall
include the feminine and neuter genders and vice versa.

     (d)  Severability.  Every provision in this Agreement is intended to be
          ------------
severable. In the event that any provision of this Agreement shall be held to be
invalid, the same shall not affect in any respect whatsoever the validity of the
remaining provisions of this Agreement.

     (e)  Captions.  Any section or paragraph titles or captions contained in
          --------
this Agreement are for convenience only and shall not be deemed a part of the
context of this Agreement.

     (f)  Entire Agreement.  This Agreement together with the Partnership
          ----------------
Agreement contains the entire understanding and agreement between the parties
and supersedes any prior written or oral agreements between them respecting the
subject matter contained herein. There are no representations, agreements,
arrangements or understandings, oral or written, between and among the parties
hereto relating to the subject matter of this Agreement which are not fully
expressed herein or therein.

     (g)  No Waiver.  The failure of any party to insist upon strict performance
          ---------
of a covenant hereunder or of any obligation hereunder, irrespective of the
length of time for which such failure continues, shall not be a waiver of such
party's right to demand strict compliance in the future. No consent or waiver,
express or implied, to or of any breach or default in the performance of any
obligation hereunder shall constitute a consent or waiver to or of any other
breach or default in the performance of the same or any obligation hereunder.

     (h)  Amendment.  This Agreement may be changed, modified or amended only by
          ---------
an instrument in writing duly executed by all of the parties hereto. Any such
amendment shall be effective as of such date as may be determined by the parties
hereto.

     (i)  Enforcement.  The Company may enforce this Agreement pursuant to the
          -----------
provisions of the Agreement of Limited Partnership of the Partnership, provided
that in the event of a dispute, either General Partner of the Company shall have
the right to enforce the provisions hereof.

     (j)  Choice of Law.  THIS AGREEMENT AND THE RIGHTS AND OBLIGATIONS OF THE
          -------------
PARTIES HEREUNDER SHALL BE GOVERNED BY TEXAS LAW.

                                       13
<PAGE>

     IN WITNESS WHEREOF, the parties have executed this Agreement or caused the
same to be executed by their duly authorized corporate officers, all as of the
day and year first above written.


"Executive"                             /s/ Jack D. Hightower
                                        ----------------------------------------
                                        Jack D. Hightower



"Company"                               TITAN RESOURCES HOLDINGS, INC.



                                        By: /s/ Phillip Ballard
                                           -------------------------------------
                                           Phillip Ballard
                                           Vice President

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