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                                                                    EXHIBIT 10.4

                               VOTING AGREEMENT

     VOTING AGREEMENT ("Agreement") dated as of December 13, 1999 between
Union Oil Company of California, a California corporation ("Union Oil"), and
Jack D. Hightower (the "Stockholder").

                             W I T N E S S E T H:

     WHEREAS, as of the date hereof, the Stockholder beneficially owns an
aggregate of 4,389,690 shares of Common Stock, par value $.01 per share ("Titan
Common Stock"), of Titan Exploration, Inc., a Delaware corporation ( "Titan")
(such shares of Titan Common Stock and any shares of Titan Common Stock acquired
by the Stockholder after the date hereof, the "Shares");

     WHEREAS, Union Oil is prepared to enter into an Agreement and Plan of
Merger among Titan Resources Holdings, Inc., a Delaware corporation and wholly
owned subsidiary of Union Oil ("Resources"), TRH, Inc., a Delaware corporation
and wholly owned subsidiary of Resources ("Sub"), and Titan (as amended from
time to time, the "Merger Agreement") providing for the merger of Titan with Sub
(the "Merger"), as a result of which Titan will become a wholly owned subsidiary
of Resources;

     WHEREAS, in order to encourage Union Oil, Resources and Sub to enter
into the Merger Agreement with Titan, the Stockholder is willing to enter into
certain arrangements with respect to the Shares;

     NOW, THEREFORE, in consideration of the premises set forth above, the
mutual promises set forth below, and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

     1.   Stockholder's Support of the Merger. From the date hereof until the
earliest to occur of (i) the termination of the Merger Agreement, and (ii) the
consummation of the Merger:

          (a)  The Stockholder agrees that it will maintain beneficial
     ownership of the Shares and will not, directly or indirectly, (i) sell,
     transfer, pledge or otherwise dispose of any Shares to any person other
     than Union Oil or its designee unless such person shall have agreed in
     writing to be bound by the terms of this Agreement, or (ii) grant a proxy
     with respect to any Shares to any person other than Union Oil or its
     designee, or grant an option
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     with respect to any of the foregoing, or enter into any other agreement or
     arrangement with respect to any of the foregoing.

          (b)  The Stockholder will not initiate, solicit or encourage
     (including by way of furnishing information or assistance), or take any
     other action to facilitate, any inquiries or the making of any proposal
     relating to, or that may reasonably be expected to lead to, any merger,
     consolidation, share exchange, business combination or similar transaction
     involving Titan or any of its subsidiaries or the acquisition in any
     manner, directly or indirectly, of a material equity interest in any voting
     securities of, or a substantial portion of the assets of, Titan or any of
     its Subsidiaries, other than the transactions contemplated by this
     Agreement or the Merger Agreement (a "Competing Transaction"), or enter
     into discussions or negotiate with any person or entity in furtherance of
     such inquiries or to obtain a Competing Transaction, or agree to, or
     endorse, any Competing Transaction, or authorize or permit any investment
     banker, financial advisor, attorney, accountant or other representative
     retained by the Stockholder to take any such action. The Stockholder shall
     promptly notify Union Oil of all relevant terms of any such inquiries or
     proposals received by the Stockholder or by any such investment banker,
     financial advisor, attorney, accountant or other representative relating to
     any of such matters and if such inquiry or proposal is in writing, the
     Stockholder shall deliver or cause to be delivered to Union Oil a copy of
     such inquiry or proposal.

          (c)  The Stockholder agrees that it will vote all Shares (i) in favor
     of approval of the Merger Agreement and any other matters that are
     conditions to consummation of the Merger and (ii) subject to the provisions
     of paragraph (d) below, against any combination proposal or other matter
     that may interfere or be inconsistent with the Merger (including without
     limitation a Competing Transaction).

          (d)  The Stockholder agrees that, if requested by Union Oil, the
     Stockholder will not attend and the Stockholder will not vote the Shares at
     any annual or special meeting of stockholders at which a Competing
     Transaction is being considered, or execute any written consent of
     stockholders relating directly or indirectly to a Competing Transaction,
     during such period.

          (e)  The Stockholder acknowledges that the terms of this Agreement
     will be required to be described, and this Agreement will be required to be
     filed, in certain securities law filings relating to the Merger.

          (f)  To the extent inconsistent with the provisions of this Section 1,
     the Stockholder hereby revokes any and all proxies with respect to the
     Shares or any other voting securities of Titan held by the Stockholder.

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     Notwithstanding anything to the contrary set forth herein, this Agreement
shall not restrict the Stockholder from acting in accordance with his fiduciary
duties as an officer or director of Titan.

     In addition, this Agreement shall not be effective with respect to such
number of Shares, if any, as shall be necessary so that none of the entry into
this Agreement or the existence of this Agreement or the rights of Union Oil
hereunder would cause Union Oil or any of its Affiliates to be deemed to be an
"Acquiring Person" within the meaning of the Rights Agreement dated as of June
10, 1999 between Titan and First Union National Bank, as such Rights Agreement
shall be amended from time to time.

     2.   Miscellaneous

          (a)  The Stockholder, on the one hand, and Union Oil, on the other,
     acknowledge and agree that irreparable damage would occur if any of the
     provisions of this Agreement were not performed in accordance with their
     specific terms or were otherwise breached. It is accordingly agreed that
     the parties shall be entitled to an injunction or injunctions to prevent
     breaches of the provisions of this Agreement and to enforce specifically
     the terms and provisions hereof in any court of the United States or any
     state thereof having jurisdiction, in addition to any other stockholder to
     which they may be entitled at law or equity.

          (b)  Descriptive headings are for convenience only and shall not
     control or affect the meaning or construction of any provision of this
     Agreement.

          (c)  All notices, consents, requests, instructions, approvals and
     other communications provided for herein shall be validly given, made or
     served, if in writing and delivered personally, by telecopy or sent by
     registered mail, postage prepaid:

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          If to Union Oil:

               Union Oil Company of California
               One Sugar Creek Place
               14141 Southwest Freeway
               Sugar Land, Texas 77478
               Attention: Mr. Phil Ballard
               Facsimile No.: (281) 287-5170

          with a copy to:

               Union Oil Company of California
               2141 Rosecrans Avenue, Suite 4000
               El Segundo, California 90245
               Attention: (1) General Counsel, and
                          (2) Vice President, Corporate Development
               Fax No: (310) 726-7819


          If to the Stockholder:

               Titan Resources Holdings, Inc.
               500 West Texas
               Suite 200
               Midland, Texas 79701
               Attention: Jack D. Hightower
               Fax: (915) 687-3863

     or to such other address or telecopy number as any party may, from time to
     time, designate in a written notice given in a like manner. Notice given by
     telecopy shall be deemed delivered on the day the sender receives telecopy
     confirmation that such notice was received at the telecopy number of the
     addressee. Notice given by mail as set out above shall be deemed delivered
     three days after the date the same is postmarked.

          (d)  From and after the termination of this Agreement, the covenants
     of the parties set forth herein shall be of no further force or effect and
     the parties shall be under no further obligation with respect thereto.

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          (e)  Definitions. For purposes of this Agreement, the following terms
     shall have the following meanings:

               (i)   Merger. "Merger" shall mean the transaction referred to in
          the second whereas clause of this Agreement, or any amendment to or
          modification that does not adversely affect the economic value of the
          Merger to the Stockholder pursuant to the transaction set forth in the
          Merger Agreement.

               (ii)  Person. A "person" shall mean any individual, firm,
          corporation, partnership, trust, limited liability company or other
          entity.

          (f)  Due Authorization; No Conflicts. The Stockholder hereby
     represents and warrants to Union Oil as follows: the Stockholder has full
     power and authority to enter into this Agreement. Neither the execution or
     delivery of this Agreement nor the consummation of the transactions
     contemplated herein will (a) conflict with or result in a breach, default
     or violation of any agreement, proxy, document, instrument, judgment,
     decree, order, governmental permit, certificate, license, law, statute,
     rule or regulation to which the Stockholder is a party or to which it is
     subject, (b) result in the creation of any lien, charge or other
     encumbrance on any Shares or (c) require the Stockholder to obtain the
     consent of any private non-governmental third party. No consent, action,
     approval or authorization of, or registration, declaration or filing with,
     any governmental department, commission, agency or other instrumentality or
     any other person or entity is required to authorize, or is otherwise
     required in connection with, the execution and delivery of this Agreement
     or the Stockholder's performance of the terms of this Agreement or the
     validity or enforceability of this Agreement.

          (g)  Successors and Assigns. This Agreement shall be binding upon, and
     inure to the benefit of, the parties hereto and their respective heirs,
     personal representatives, successors and assigns, but, except as
     contemplated pursuant to paragraph 1(a), shall not be assignable by any
     party hereto without the prior written consent of the other parties hereto.

          (h)  Waiver. No party may waive any of the terms or conditions of this
     Agreement except by a duly signed writing referring to the specific
     provision to be waived.

          (i)  Governing Law. This Agreement shall be governed by, and construed
     and enforced in accordance with, the laws of the State of Delaware.

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          (j)  Entire Agreement. This Agreement constitutes the entire
     agreement, and supersedes all other and prior agreements and
     understandings, both written and oral, among the parties hereto.

          (k)  Counterparts. This Agreement may be executed in two or more
     counterparts, each of which shall be deemed an original but all of which
     shall constitute one and the same instrument.

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     IN WITNESS WHEREOF, the Stockholder and Union Oil have each caused this
Agreement to be duly executed as of the day and year first above written.

                                        UNION OIL COMPANY OF CALIFORNIA


                                        By: /s/ Timothy H. Ling
                                           -----------------------------
                                           Timothy H. Ling
                                           Executive Vice President, North
                                           American Energy Operations and Chief
                                           Financial Officer


                                        JACK D. HIGHTOWER



                                        /s/ Jack D. Hightower
                                        --------------------------------
                                        Jack D. Hightower
                                        President and Chief Executive Officer

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