<PAGE>

                             Pure Resources, Inc.

                                 Exhibit 10.6
                                 ------------

Form of Confidentiality and Non-Compete Agreement dated May 25, 2000 between
Pure Resources, Inc., Titan Exploration, Inc. and Pure Resources I, Inc.
(formerly Titan Resources I, Inc.) and each of certain officers
<PAGE>

                                                                    Exhibit 10.6

                   CONFIDENTIALITY AND NON-COMPETE AGREEMENT

     This CONFIDENTIALITY AND NON-COMPETE AGREEMENT (the "Agreement") is made by
and between Pure Resources, Inc., Titan Exploration, Inc., and Titan Resources
I, Inc., (collectively, along with its or their subsidiaries, successors, and
assigns, the "Related Parties"), and [See Schedule I attached] ("Employee").

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

     WHEREAS, Titan Resources I, Inc. ("Employer"), a wholly-owned subsidiary of
Titan, currently employs and desires to continue to employ Employee after the
consummation of the transactions contemplated by the Merger Agreement, and
Employee desires to continue his employment with Employer;

     WHEREAS, Employee acknowledges that, as a result of the consummation of the
transactions contemplated by the Merger Agreement, he will become privy to
various business opportunities, economic and trade secrets, and confidential and
proprietary business information of the Related Parties, his knowledge of and
access to which are essential to the performance of his job duties;

     NOW, THEREFORE, in consideration of Employee's access to various business
opportunities, economic and trade secrets, and confidential and proprietary
business information of the Related Parties, and the letter agreement between
Employee and Employer of even date herewith, the Related Parties and Employee,
intending to be legally bound, agree as follows:

     1.   Contingency of Agreement; Effective Date of Agreement.  This Agreement
          -----------------------------------------------------
will become effective on the date of consummation of the transactions
contemplated by the Merger Agreement (the "merger") and shall be contingent upon
the consummation of the merger (the "Effective Date").

     2.   Business Opportunities and Intellectual Property.
          ------------------------------------------------

     (a)  Employee shall promptly disclose to Employer, its successors, assigns,
or designees, all "Business Opportunities" and "Intellectual Property" (as
defined below).

     (b)  Employee hereby assigns and agrees to assign to Employer, its
successors, assigns, or designees, all of Employee's right, title, and interest
in and to all Business Opportunities and Intellectual Property, and further
acknowledges and agrees that all Business Opportunities and Intellectual
Property constitute the exclusive property of the Related Parties.
<PAGE>

     (c)  For purposes hereof "Business Opportunities" shall mean all business
ideas, prospects, proposals or other opportunities pertaining to the lease,
acquisition, exploration, production, gathering or marketing of hydrocarbons and
related products and the exploration potential of geographical areas on which
hydrocarbon exploration prospects are located, which are developed by Employee
during any period that Employee is or was employed by Employer or one of the
other Related Parties (the "Employment Term") or originated by any third party
and brought to the attention of Employee, together with information relating
thereto (including, without limitation, geological and seismic data and
interpretations thereof, whether in the form of maps, charts, logs,
seismographs, calculations, summaries, memoranda, opinions or other written or
charted means).

     (d)  For purposes hereof "Intellectual Property" shall mean all ideas,
inventions, discoveries, processes, designs, methods, substances, articles,
computer programs, and improvements (including, without limitation, enhancements
to, or further interpretation or processing of, information that was in the
possession of Employee prior to the date of this Agreement), whether or not
patentable or copyrightable, which do not fall within the definition of Business
Opportunities, which Employee discovers, conceives, invents, creates, or
develops, alone or with others, during any Employment Term, if such discovery,
conception, invention, creation, or development (i) occurs or occurred in the
course of Employee's employment with Employer or one of the other Related
Parties, (ii) occurs or occurred with the use of any of the Related Parties'
time, materials, or facilities, or (iii) in the opinion of the Board of
Directors of Employer, relates or pertains in any way to Employer's or one of
the other Related Parties' purposes, activities, or affairs.

     3.   Non-Compete Obligations During Employment Term.  Employee agrees that
          ----------------------------------------------
during any Employment Term, Employee will not, other than through Employer or
one of the other Related Parties, engage or participate in any manner, whether
directly or indirectly through any family member or as an employee, employer,
consultant, agent, principal, partner, more than one percent shareholder,
officer, director, licensor, lender, lessor or in any other individual or
representative capacity, in any business or activity which is engaged in
leasing, acquiring, exploring, producing, gathering or marketing hydrocarbons
and related products; provided that this Section 3 shall not apply to personal
oil and gas investments owned by Employee, his family members, or his controlled
affiliates as of the date this Agreement is executed and of which Employer is
aware.

     4.   Confidentiality Obligations.
          ---------------------------

     (a)  Employee hereby acknowledges that all trade secrets and confidential
and proprietary business information of the Related Parties (collectively
referred to herein as "Confidential Information") constitutes valuable, special
and unique assets of the Related Parties' business, and that access to and
knowledge of such Confidential Information is essential to the performance of
Employee's job duties.  Employee agrees that during any Employment Term and
during the two-year period following the date of termination of Employee's
employment with Employer or one of the other Related Parties (the "Termination
Date"), Employee will hold the Confidential Information in strict confidence and
will not publish, disseminate or otherwise disclose, directly or indirectly, to
any person other than the Related Parties and their respective officers,
directors and employees or otherwise in proper performance of Employee's job
duties, any Confidential Information or use any
<PAGE>

Confidential Information for Employee's own personal benefit or for the benefit
of anyone other than the Related Parties.

     (b)  For purposes of this Section 4, it is agreed that Confidential
Information includes, without limitation, any information heretofore or
hereafter acquired, developed or used by any of the Related Parties relating to
Business Opportunities or Intellectual Property or other geological,
geophysical, economic, financial or management aspects of the business,
operations, properties or prospects of the Related Parties, whether oral or in
written form in a "Related Parties' Business Records" (as defined in Section 6
below), but shall exclude any information which has become part of the common
knowledge or understanding in the oil and gas industry or otherwise in the
public domain (other than from disclosure by Employee in violation of this
Agreement) and provided further that this Section 4 shall not be applicable to
the extent Employee is required to testify in a judicial or regulatory
proceeding pursuant to the order of a judge or administrative law judge after
Employee requests that such Confidential Information be preserved and after
prior notice to the Related Parties.

     5.   Post Employment Non-Compete And Non-Solicitation Obligations.
          ------------------------------------------------------------

     (a)  Employee agrees that during the two-year period following the
Termination Date, he will not compete, either directly or indirectly with any of
the Related Parties for any acquisition, prospect, or project that any of the
Related Parties was pursuing prior to the Termination Date.

     (b)  Employee agrees that during the two-year period following the
Termination Date, he will not solicit, entice, persuade or induce, directly or
indirectly, any employee (or person who within the preceding ninety (90) days
was an employee) of any of the Related Parties or any other person who is under
contract with or rendering services to any of the Related Parties, to (i)
terminate his or her employment by, or contractual relationship with, such
person, (ii) refrain from extending or renewing the same (upon the same or new
terms), (iii) refrain from rendering services to or for such person, (iv) become
employed by or to enter into contractual relations with any persons other than
such person, or (v) enter into a relationship with a competitor of any of the
Related Parties.

     6.   Business Records.
          ----------------

     (a)  Employee agrees to promptly deliver to Employer or its designee, upon
termination of his employment by Employer or any of the Related Parties, or at
any other time when any of the Related Parties so requests, all documents
relating to the business of the Related Parties, including, without limitation:
all geological and geophysical reports and related data such as maps, charts,
logs, seismographs, seismic records and other reports and related data,
calculations, summaries, memoranda and opinions relating to the foregoing,
production records, electric logs, core data, pressure data, lease files, well
files and records, land files, abstracts, title opinions, title or curative
matters, contract files, notes, records, drawings, manuals, correspondence,
financial and accounting information, customer lists, statistical data and
compilations, patents, copyrights, trademarks, trade names, inventions,
formulae, methods, processes, agreements, contracts, manuals or any other
documents relating to the business of the Related Parties (collectively, the
"Related Parties' Business Records"), and all copies thereof and therefrom.
<PAGE>

     (b)  Employee confirms that all of the Related Parties' Business Records
(and all copies thereof and therefrom) which are required to be delivered to
Employer or its designee pursuant to this Section constitute the exclusive
property of Employer and the other Related Parties.

     (c)  The obligation of confidentiality set forth in Section 4 shall
continue notwithstanding Employee's delivery of any such documents to Employer
and its designee.

     (d)  Notwithstanding the foregoing provisions of this Section 6 or any
other provision of this Agreement, Employee shall be entitled to retain any
written materials received by Employee in the capacity as a shareholder of Pure.

     7.   Miscellaneous.
          -------------

     (a)  The invalidity or non-enforceability of any provision of this
Agreement in any respect shall not affect the validity or enforceability of this
Agreement in any other respect or of any other provision of this Agreement. In
the event that any provision of this Agreement shall be held invalid or
unenforceable by a court of competent jurisdiction by reason of the geographic
or business scope or the duration thereof, such invalidity or unenforceability
shall attach only to the scope or duration of such provision and shall not
affect or render invalid or unenforceable any other provision of this Agreement,
and, to the fullest extent permitted by law, this Agreement shall be construed
as if the geographic or business scope or the duration of such provision had
been more narrowly drafted so as not to be invalid or unenforceable.

     (b)  Employee acknowledges that the Related Parties' remedy at law for any
breach of the provisions of this Agreement is and will be insufficient and
inadequate and that the Related Parties shall be entitled to equitable relief,
including by way of temporary and permanent injunction, in addition to any
remedies the Related Parties may have at law.

     (c)  The existence of any claim or cause of action of Employee against any
of the Related Parties or any officer, director, or shareholder of any of the
other Related Parties, whether predicated on Employee's employment or otherwise,
shall not constitute a defense to the enforcement by any of the Related Parties
of the covenants of Employee contained in this Agreement.  In addition, the
provisions of this Agreement shall continue to be binding upon Employee in
accordance with their terms, notwithstanding the termination of Employee's
employment with Employer or any of the other Related Parties for any reason.

     (d)  The parties to this Agreement agree that the limitations contained in
Section 5 with respect to time, geographical area, and scope of activity are
reasonable.  However, if any court shall determine that the time, geographical
area, or scope of activity of any restriction contained in Section 5 is
unenforceable, it is the intention of the parties that such restrictive covenant
set forth herein shall not thereby be terminated but shall be deemed amended to
the extent required to render it valid and enforceable.

     (e)  This Agreement may be assigned or transferred by any of the Related
Parties, and shall inure to the benefit of the successors and assigns of any of
the Related Parties.
<PAGE>

     (f)  This Agreement is not intended to be and does not constitute a
contract or promise of employment or continued employment for any specified term
or other than at will.

     (g)  This Agreement may not be altered or amended except by a writing, duly
executed by the party against whom such alteration or amendment is sought to be
enforced.

     (h)  This Agreement may be executed in counterparts, each of which shall be
an original and all of which together shall constitute one and the same
instrument.

<PAGE>

     IN WITNESS WHEREOF, each of the parties hereto has executed this Agreement
in multiple counterparts on the 25th day of May, 2000.

                              PURE RESOURCES, INC.


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

                              TITAN EXPLORATION, INC.


                              By: /s/ Jack Hightower*
                                 ----------------------------------------
                                 Name: Jack Hightower
                                 Title: President

                                  [*Note: agreement of Jack Hightower was
                                  signed on behalf of Titan Exploration, Inc.
                                  and Titan Resources I, Inc. by
                                  William White, Vice President]

                              TITAN RESOURCES I, INC.


                              By: /s/ Jack Hightower *
                                 ----------------------------------------
                                 Name: Jack Hightower
                                 Title: President

                                  [*Note: agreement of Jack Hightower was
                                  signed on behalf of Titan Exploration, Inc.
                                  and Titan Resources I, Inc. by
                                  William White, Vice President]


                              EMPLOYEE



                              /s/ [See Schedule I attached]
                              -------------------------------------------
                              [See Schedule I attached]
<PAGE>

                                   Schedule I

Name of Employee
----------------

John L. Benfatti
Dan P. Colwell
Jack D. Hightower
Darin Holderness
Thomas H. Moore
Susan D. Rowland
George G. Staley
William K. White
Rodney L. Woodard