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                                                                    EXHIBIT 4.1

                         AMENDMENT AND WAIVER AGREEMENT

     THIS AMENDMENT AND WAIVER AGREEMENT, dated as of September 10, 2003, is
executed by and among TOM BROWN, INC., a Delaware corporation (the "Company"),
UNION OIL COMPANY OF CALIFORNIA, a California corporation ("Unocal"), and
CHICAGO CARBON COMPANY, an Illinois general partnership ("CCC").

                                    RECITALS

     A.   The Company and Unocal entered into a Stock Ownership and
Registration Rights Agreement dated as of June 29, 1999, which Agreement was
supplemented by an Addendum dated as of September 30, 1999 by and among the
Company, Unocal and CCC (collectively, the "Agreement").

     B.   Pursuant to Section 4.2(a) of the Agreement, in the event that the
Company issues, sells or transfers shares of common stock of the Company (the
"TBI Common Stock"), CCC (as Unocal's successor in interest) has the right to
purchase additional shares from the Company to maintain its percentage
ownership of TBI Common Stock at the level it was immediately prior to the time
of each such issuance, sale or transfer.

     C.   The Company has commenced and intends to consummate a public offering
of shares of TBI Common Stock (the "Offering") pursuant to an underwritten
offering led by JP Morgan and CCC will be a selling stockholder in such
offering.

                                   AGREEMENTS

     NOW, THEREFORE, in consideration of the agreements set forth above,

     1.   Unocal and CCC hereby waive any and all rights they may have to
acquire additional shares from the Company pursuant to the provisions set forth
in Section 4.2(a) of the Agreement as a result of the issuance and sale of
shares in the Offering or pursuant to any employee benefit plan of the Company.

     2.   The Agreement is hereby amended to add the following sentence to the
end of Section 4.2(a):

          Notwithstanding anything contained herein, neither Unocal nor any of
          its affiliates shall have the right to acquire shares of TBI Common
          Stock from TBI as a result of any issuance, sale or transfer of shares
          of TBI Common Stock pursuant to any employee benefit plan of TBI.

     (3)  Neither Unocal nor CCC waives any other rights or privileges under the
Agreement and, except for the specific waiver and amendment made herein, the
Agreement shall remain in full force and effect without modification.

                                      -1-
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     IN WITNESS WHEREOF, the parties have caused this Waiver to be duly
executed as of the date set forth above.

                                   TOM BROWN, INC.


                                   By: /s/ Daniel G. Blanchard
                                       ----------------------------------
                                   Name: Daniel G. Blanchard
                                   Title: Executive Vice President and
                                          Chief Financial Offer


                                   UNION OIL COMPANY OF CALIFORNIA


                                   By: /s/ Douglas M. Miller
                                       -----------------------------------
                                   Name: Douglas M. Miller
                                   Title: Vice President, Corporate
                                          Development


                                   CHICAGO CARBON COMPANY


                                   By: Midwest 76, Inc.



                                   By: /s/ Darrell D. Chessum
                                       -------------------------------------
                                   Name:  Darrell D. Chessum
                                   Title: Treasurer


                                   By: Lemont Carbon, Inc.




                                   By: /s/ Darrell D. Chessum
                                       --------------------------------------
                                   Name:  Darrell D. Chessum
                                   Title: Treasurer


                                   By: Midwest Natural Gas Pipeline Company



                                   By: /s/ Gary R. Miller
                                       --------------------------------

                                   Name: Gary R. Miller
                                        -------------------------------

                                   Title: Assistant Comptroller
                                         ------------------------------


                                   Constituting all of the partners of the
                                   Chicago Carbon Company