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                                                                    Exhibit 10.6

                       FIRST AMENDMENT TO RIGHTS AGREEMENT
             AND CERTIFICATION OF COMPLIANCE WITH SECTION 27 THEREOF

         This Amendment, dated as of October 28, 2000 (the "AMENDMENT"), to the
Rights Agreement, dated as of February 24, 1996 (the "AGREEMENT"), between Basin
Exploration, Inc., a Delaware corporation (the "COMPANY"), and Corporate Stock
Transfer, Inc. (the "RIGHTS AGENT"). Capitalized terms used in this Amendment
without definition shall have the respective meanings ascribed to them in the
Agreement.

         Pursuant to Section 27 of the Agreement, this Amendment is being
executed by the Company and the Rights Agent for the purpose of amending the
Agreement as set forth below:

         The Agreement is hereby amended as follows:

         1.       Section 1(a) shall be amended by inserting "(i)" following the
phrase "Notwithstanding the foregoing," and inserting the following at the end
of the sentence beginning with such phrase::

                  "and (ii) neither Stone Energy Corporation, a Delaware
                  corporation ("ACQUIROR"), or Partner Acquisition Corp., a
                  Delaware corporation ("MERGER SUB"), or any Affiliates or
                  Associates of Acquiror or Merger Sub, shall be an Acquiring
                  Person solely by virtue of (A) the execution of the Agreement
                  and Plan of Merger, dated as of October 28, 2000 (the "MERGER
                  AGREEMENT"), by and among Acquiror, Merger Sub and the
                  Company, (B) the acquisition of Common Shares of the Company
                  pursuant to the Merger (as defined in the Merger Agreement),
                  (C) the execution of the Company Voting Agreement, dated the
                  date of the Merger Agreement, among the Company, Acquiror and
                  the Company stockholders signatory thereto (the "COMPANY
                  VOTING AGREEMENT") or the Acquiror Voting Agreement, dated the
                  date of the Merger Agreement, among the Company, Acquiror and
                  the Acquiror stockholders signatory thereto (the "ACQUIROR
                  VOTING AGREEMENT"), or (D) the consummation of the Merger (as
                  defined in the Merger Agreement) or of the other transactions
                  contemplated in the Merger Agreement, the Company Voting
                  Agreement or the Acquiror Voting Agreement."

         2.       Section 1(s) shall be amended by inserting the following at
the end of the definition of "Shares Acquisition Date":

                  "Notwithstanding the foregoing, no Shares Acquisition Date
                  shall occur solely by reason of (A) the execution of the
                  Merger Agreement, (B) the acquisition of Common Shares of the
                  Company pursuant to the Merger (as defined in the Merger
                  Agreement), (C) the execution of the Company Voting Agreement
                  or the Acquiror Voting Agreement, or (D) the consummation of
                  the Merger (as defined in the Merger Agreement) or of the
                  other transactions contemplated in the Merger Agreement, the
                  Company Voting Agreement or the Acquiror Voting Agreement."


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         3.       Section 3(a) shall be amended by inserting the following at
the end of the subsection:

                  "Notwithstanding the foregoing or any provision to the
                  contrary in this Agreement, a Distribution Date shall not
                  occur solely by reason of (A) the execution of the Merger
                  Agreement, (B) the acquisition of Common Shares of the Company
                  pursuant to the Merger (as defined in the Merger Agreement),
                  (C) the execution of the Company Voting Agreement or the
                  Acquiror Voting Agreement, or (D) the consummation of the
                  Merger (as defined in the Merger Agreement) or of the other
                  transactions contemplated in the Merger Agreement, the Company
                  Voting Agreement or the Acquiror Voting Agreement."

         4.       Section 7(a) shall be amended by deleting the word "or"
immediately preceding clause (iii) thereto and replacing all of clause (iii) and
the text following clause (iii), with "(iii) at the Effective Time (as defined
in the Merger Agreement) or (iv) the time at which such Rights are exchanged as
provided in Section 24 hereof. The Company, upon having knowledge thereof, will
promptly notify the Rights Agent of the anticipated Effective Time."

         5.       Section 11(a)(ii) shall be amended by inserting the following
in the first parenthetical following the phrase "Flip In Event":

                  "; provided, however, that no Flip In Event shall occur solely
                  by reason of (A) the execution of the Merger Agreement, (B)
                  the acquisition of Common Shares of the Company pursuant to
                  the Merger (as defined in the Merger Agreement), (C) the
                  execution of the Company Voting Agreement or the Acquiror
                  Voting Agreement, or (D) the consummation of the Merger (as
                  defined in the Merger Agreement) or of the other transactions
                  contemplated in the Merger Agreement, the Company Voting
                  Agreement or the Acquiror Voting Agreement."


         6.       Section 13 shall be amended by inserting the following
subsection at the end thereof:

                  "(f) No event as described in Section 13(a)(i), (ii) or (iii)
                  shall occur solely by reason of (A) the execution of the
                  Merger Agreement, (B) the acquisition of Common Shares of the
                  Company pursuant to the Merger (as defined in the Merger
                  Agreement), (C) the execution of the Company Voting Agreement
                  or the Acquiror Voting Agreement, or (D) the consummation of
                  the Merger (as defined in the Merger Agreement) or of the
                  other transactions contemplated in the Merger Agreement, the
                  Company Voting Agreement or the Acquiror Voting Agreement."

         7.       This Amendment shall be deemed effective as of October 28,
2000 as if executed by both parties hereto on such date.


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         8.       This Amendment shall be deemed to be a contract made under the
laws of the State of Delaware and for all purposes shall be governed by and
construed in accordance with the laws of such State applicable to contracts to
be made and performed entirely within such State.

         9.       This Amendment may be executed in any number of counterparts
and each of such counterparts shall for all purposes be deemed to be an
original, and all such counterparts shall together constitute but one and the
same instrument.

         10.      Except as amended hereby, the Agreement shall remain in full
force and effect.

         The undersigned officer of the Company, being an appropriate officer of
the Company and authorized to do so by resolution of the Board of Directors of
the Company dated as of October 25, 2000, hereby certifies to the Rights Agent
that these amendments are in compliance with the terms of Section 27 of the
Agreement.


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         IN WITNESS WHEREOF, the parties have caused this Amendment to be
executed and attested, all as of the day and year first above written.



                                            BASIN EXPLORATION, INC.


                                            By:  _______________________________
                                                 Name:
                                                 Title:



ATTEST:


By:  _________________________________________
     Name:  Howard L. Boigon
     Title: Vice President, General Counsel
            And Secretary



                                            CORPORATE STOCK TRANSFER, INC., as
                                            Rights Agent


                                            By:  _______________________________
                                                 Name:
                                                 Title:


ATTEST:


By:  _______________________________________
     Name:
     Title: