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                                                                    Exhibit 10.6

                              PURE RESOURCES, INC.
                                500 West Illinois
                              Midland, Texas 79701


                                January 30, 2001



Union Oil Company of California
2141 Rosecrans Avenue, Suite 4000
El Segundo, California 90245
Attention: Mr. Terry Dallas, Chief Financial Officer

     Re:  Pure Resources, Inc. - Business Opportunities Agreement

Ladies and Gentlemen:

     Reference is made to the Business Opportunities Agreement (the "Agreement")
dated as of December 13, 1999 among Union Oil Company of California ("Union
Oil"), Pure Resources, Inc. (formerly named Titan Resources Holdings, Inc.) (the
"Company"), TRH, Inc., and Titan Exploration, Inc.  Capitalized terms used and
not otherwise defined herein shall have the meanings given to them in the
Agreement.  The Agreement was entered into to address certain legal requirements
and concerns as well as for certain practical business purposes.   Although this
letter does request a limited waiver of the Agreement, we wish to make it clear
that we understand that the Agreement will remain in effect after any grant of a
limited waiver  and that we will continue to remain focused on the business we
conduct in the Designated Area and any other area that you may permit us to
operate in pursuant to the limited waiver.

     As you are aware, the Company proposes to acquire, through a wholly-owned
subsidiary of the Company, certain of the Assets (as defined below) and to
acquire a majority of the partnership interests in a limited partnership (the
"Partnership") that will own certain of the Assets (as defined). As used in this
letter, "Assets" means certain oil and gas fee mineral interests, royalty
interests, oil and gas leasehold interests and related contracts and assets
located in Alabama, Arkansas, Florida, Louisiana, Mississippi, Oklahoma, Texas
and the offshore area of the Gulf of Mexico (with limited holdings located in
Michigan, New Mexico, New York, North Dakota, Pennsylvania and Wyoming)
currently owned by International Paper Company or its affiliates (collectively,
the "Assets").  Part 1 of Annex A to this letter identifies the counties in
Michigan, New Mexico, New York, North Dakota, Pennsylvania and Wyoming in which
Assets are located, and the location of the other Assets is generally indicated
on the map attached to this letter as part 2 of Annex A.  Certain of the
contractual rights to be acquired with the Assets that may give the Company
rights to invest or acquire interests in opportunities outside of the Designated
Area and the locations set forth on Annex A, are set forth on Annex B to this
letter.

     Pursuant to Section 1 of the Agreement, the Company agreed that, except
with the consent of Union Oil (which it may withhold in its sole discretion),
neither the Company nor its subsidiaries will engage in any business other than
the E&P Business and none of them will pursue any business
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January 30, 2001
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opportunity  that  involves  any direct or  indirect  ownership  interest in any
properties located outside the Designated Area. Notwithstanding Section 1 or any
other  provision in the  Agreement,  we hereby  request your limited  waiver and
consent  (a) to the  consummation  of the  Company's  acquisition  (directly  or
through  subsidiaries)  of the Assets  and the  Company's  (directly  or through
subsidiaries)  conducting  the E&P  Business on  properties  included  among the
Assets following such acquisition  (collectively,  the "Acquisition") and (b) to
the Company's (and its subsidiaries') engaging in the "Extended Business," which
term means E&P Business  opportunities  that directly arise out of the ownership
or operation of the Assets. The term "Extended  Business"  includes  contractual
rights and  obligations  under currently  existing  contracts (but not rights or
obligations  first  arising  out of any  amendment  to such  existing  contracts
entered into after the date hereof)  included within the Assets and described in
Annex B and other  opportunities  that primarily relate to land or minerals that
are  included  within the  Assets or located  within two (2) miles of any of the
Assets provided that under no circumstances  shall the term "Extended  Business"
include  any  investment  in or  acquisition  related  to  opportunities  in the
off-shore  areas of the Gulf of Mexico.  By signing below,  Union Oil hereby (1)
evidences its limited waiver of the application of the Agreement's  restrictions
to the Acquisition and the Extended  Business (but not as to any other expansion
outside the Designated Area that is not clearly and  unequivocally  contemplated
by the Acquisition and the Extended  Business) and (2) acknowledges that neither
the Acquisition nor the Extended  Business shall be deemed a breach or violation
of the Agreement.

     We hereby acknowledge that if you grant the limited waiver requested above
or any more restrictive waiver, that such limited waiver will only apply to the
Acquisition and the Extended Business and in no way shall serve to waive any
provision of the Agreement that may be applicable to future transactions or
investments by the Company that are not included within the Acquisition or the
Extended Business.  Furthermore, nothing herein shall serve as a general waiver
or be construed as amending or revising in any way the definition of "Designated
Area" in the Agreement or any other provision of the Agreement.
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January 30, 2001
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     Subject to the Company finally acquiring the Assets and as consideration
for Union Oil's limited waiver as contemplated by this letter, Pure Resources,
Inc., on behalf of itself and its subsidiaries, hereby grants Union Oil a thirty
(30) day right of first refusal (i.e., a right to match the price and terms
offered in a bona fide, third party offer received by the Company after it has
had a full opportunity to market the assets subject to such right) with respect
to (a) each proposed sale (including farm-outs) by the Company of any interest
it may hold in any of the Assets or any of the assets constituting a part of the
Extended Business that are (in either case) located in the off-shore areas of
the Gulf of Mexico, and (b) each proposed sale (other than sales of mineral
rights (ownership, servitude or royalty) or leasehold interests insofar as such
leasehold interests only cover mineral rights owned by the Company) by the
Company of any interest it may hold in any of the Assets or any of the assets
constituting a part of the Extended Business that are ( in either case ),
located within the State of Louisiana and where such sale is to be primarily for
cash consideration.  In addition to the foregoing, in the event that Union Oil
exercises its right of first refusal (as described above), Union Oil will
indemnify the Company for that portion of any tax actually paid as a result of
the right of first refusal sale and for any amount actually paid by the
Partnership or the general partner of the Partnership to International Paper
Company or one of its affiliates under the terms of the Partnership's Agreement
of Limited Partnership or under the Indemnity Agreement (as defined in such
Agreement of Limited Partnership) resulting from the treatment of such sale as
an Extraordinary Asset Disposition or a Tax Indemnified Event (each as defined
in such Agreement of Limited Partnership), that in either case would not have
been paid or become payable but for the fact that the Company and Union Oil were
affiliates at the time of the sale.

     We hereby confirm that the grant of the foregoing right of first refusal
has been approved by a majority of the independent/outside directors of the
Company.

     The limited waiver that shall be effected by Union Oil's execution below
shall automatically terminate, without further action by any party, if the
Company has not consummated the acquisition of the Assets by March 31, 2001.

     Please sign this letter in the space below, fax a signed copy to Joe
Dannenmaier of  Thompson & Knight L.L.P. (fax 214/ 969-1751) and return the
signed original to Pure Resources, Inc. c/o Joe Dannenmaier, Thompson & Knight,
L.L.P., 1700 Pacific Avenue, Suite 3300, Dallas, Texas  75201.

                                    Very truly yours,

                                    PURE RESOURCES, INC.


                                    By: /s/ Jack Hightower
                                        ---------------------------------------
                                        Jack D. Hightower,
                                        President and Chief Executive Officer
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January 30, 2001
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Accepted and agreed to:


UNION OIL COMPANY OF CALIFORNIA


By:  /s/ Terry G. Dallas
    ----------------------------------
  Name:  Terry G. Dallas
  Title: Chief Financial Officer