<PAGE>

                                                                  EXHIBIT 10.7.1
                                                                  --------------


                               December 20, 1999


To the Banks and Financial Institutions
Listed on Schedule 1 Hereto

     Re:  Credit Agreement dated as of June 24, 1999 (as amended to date, the
          "Credit Agreement") among Titan Exploration, Inc. as Borrower
          ("Borrower"), Chase Bank of Texas, National Association, as Agent and
          the Lenders Signatory Thereto

Ladies and Gentlemen:

     Reference is made to the Credit Agreement for the meanings of terms defined
therein which, unless otherwise defined in this letter, shall have the same
meanings when used herein.

     As you know, Unocal Corporation ("Unocal") and Borrower have agreed to
merge Unocal's oil and gas exploration and production assets in the Permian and
San Juan basins with Titan into a new publicly traded company to be named Pure
Energy Resources, Inc. ("Pure"). Pure will form a wholly owned subsidiary, TRH,
Inc. ("TRH"), which will be merged into Borrower, with Borrower to be the
surviving corporation. As part of the merger, Borrower's existing shareholders
will receive approximately thirty-five percent of the common stock of Pure, and
Unocal will retain approximately sixty-five percent of the common stock of Pure.
This transaction (the "Merger") is more fully described in the Agreement and
Plan of Merger dated December 13, 1999 (the "Merger Agreement") among Union Oil
Company of California, Titan Resources Holdings, Inc., TRH, and Borrower, a copy
of which is enclosed with this letter.

     As a result of the Merger, Borrower will be a wholly owned subsidiary of
Pure.  Pure will initially have one or more other subsidiaries (the "Other
Subsidiaries") that will not be owned by Borrower or any of Borrower's
Subsidiaries.  The Permian and San Juan assets to be contributed to Pure by
Unocal will initially be held in the Other Subsidiaries.

     The Merger and the other transactions contemplated in the Merger Agreement
(collectively, the "Transactions") may violate the following provisions of the
Credit Agreement:

          Section 5.03(c) restricting mergers,

          Section 5.03(k), restricting certain transactions with Affiliates, and

          Section 6.13, providing for a Change in Control to constitute an Event
of Default.

As a result of the Transactions, Unocal and its Subsidiaries may also become
ERISA Affiliates of Borrower and its Subsidiaries.

     Borrower hereby requests Lenders' and Agent's consent to the Transactions
and their waiver of the provisions of Sections 5.03(c), 5.03(k), and 6.13 of the
Credit Agreement (and any similar provisions of the Financing Documents) which
would be violated by the Transactions. Borrower further requests Lenders' and
Agent's agreement that (a) the term "ERISA Affiliate" in the Credit Agreement
will hereafter refer only to Borrower and its own Subsidiaries and (b) the term
"Maturity Date" in the Credit Agreement will hereafter refer to April 1, 2001
rather than January 1, 2001.

     Please execute a copy of this letter in the space provided below to
evidence this requested consent, waiver, and agreement:
<PAGE>

     Thank you very much for your cooperation.

Yours truly,

TITAN EXPLORATION, INC.


By: /s/ John L. Benfatti
    -----------------------------------------------
    Name:  John L. Benfatti
           ----------------------------------------
    Title: Vice President - Accounting & Controller
           ----------------------------------------


CONSENTED TO AND AGREED and
WAIVED as of the date first written above:

CHASE BANK OF TEXAS, NATIONAL
 ASSOCIATION
Individually, as Issuing Bank, and as
Administrative Agent


By: /s/ Robert C. Mertensotto
    -----------------------------------------------
    Name:  Robert C. Mertensotto
           ----------------------------------------
    Title: Managing Director
           ----------------------------------------


FIRST UNION NATIONAL BANK, Individually and as Documentation Agent

By: /s/ Robert R. Wetteroff
    -----------------------------------------------
    Name:  Robert R. Wetteroff
           ----------------------------------------
    Title: Senior Vice President
           ----------------------------------------


MORGAN GUARANTY TRUST COMPANY OF NEW YORK, Individually and as Syndication Agent

By: /s/ John Kowalczuk
    -----------------------------------------------
    Name:  John Kowalczuk
           ----------------------------------------
    Title: Vice President
           ----------------------------------------


CREDIT LYONNAIS NEW YORK BRANCH


By: /s/ Philippe Soustra
    -----------------------------------------------
    Name:  Philippe Soustra
           ----------------------------------------
    Title: Senior Vice President
           ----------------------------------------
<PAGE>

BANK ONE, TEXAS, N.A.


By: /s/ Wm. Mark Cranmer
    -------------------------------------------
    Name:  Wm. Mark Cranmer
           ------------------------------------
    Title: Vice President
           ------------------------------------



PARIBAS


By: /s/ Marian Livingston
    -------------------------------------------
    Name:  Marian Livingston
           ------------------------------------
    Title: Vice President
           ------------------------------------


UNION BANK OF CALIFORNIA, N.A.


By: /s/ Gary Shekerjian
    -------------------------------------------
    Name:  Gary Shekerjian
           ------------------------------------
    Title: Assistant Vice President
           ------------------------------------
<PAGE>

                                  SCHEDULE 1


Chase Bank of Texas, N.A.
One Chase Manhattan Plaza, 8th Floor
New York, NY 10081
Attention: Muniram Appanna Agency Services

First Union National Bank
c/o First Union Corporation
1001 Fannin Street, Suite 2255
Houston, Texas 77002-6709
Attention: Ms. Vicki Crispens

Morgan Guaranty Trust
Company of New York
60 Wall Street
New York, New York 10260
Attention: Phillip McNeal

Credit Lyonnais New York Branch
c/o Credit Lyonnais
Houston Representative Office
1000 Louisiana, Suite 5360
Houston, Texas 77002
Attention: John M. Falbo

Bank One, Texas, N.A.
1717 Main Street
Dallas, Texas 75201
Attention: Mark Cranmer

Paribas
1200 Smith Street, Suite 3100
Houston, Texas 77002
Attention: Brian Malone


Union Bank of California, N.A.
4200 Lincoln Plaza
500 North Akard
Dallas, Texas 75201
Attention: Gary Shekerjian

cc:  Chase Securities, Inc.
     707 Travis Street, 5N86
     Houston, Texas 77002
     Attention: Robert C. Mertensotto