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                                                                     EXHIBIT 4.4

                  AMENDMENT NO. 1 (this "Amendment") dated as of October 28,
2000, to the Rights Agreement (the "Rights Agreement") dated as of October 15,
1998, between Stone Energy Corporation, a Delaware corporation (the "Company"),
and ChaseMellon Shareholder Services, L.L.C., a New Jersey limited liability
company, as rights agent ("Rights Agent").

                  Pursuant to the terms of the Rights Agreement and in
accordance with Section 29 thereof, the following actions are hereby taken:

                  Section 1. Amendments to Rights Agreement. The Rights
Agreement is hereby amended as follows:

                  (a) Notwithstanding any provision of the Rights Agreement to
the contrary, none of the execution or the delivery of one or more of the Merger
Documents or the consummation of one or more of the Merger Transactions shall
cause or permit the Rights to become exercisable, the Rights to become separated
from the stock certificates to which they are attached or any operative
provision of the Rights Agreement to apply to Basin Exploration, Inc. ("Basin")
or any affiliate or associate thereof solely by reason of or in connection with
the Merger Documents or the Merger Transactions, including, without limitation,
the designation of Basin or any other person as an Acquiring Person, the
occurrence of a Distribution Date or the occurrence of a Shares Acquisition
Date.

                  (b) The definition of "Acquiring Person" in Section 1 of the
Rights Agreement is amended to add the following sentence at the end thereof:

                  "Notwithstanding anything in this Rights Agreement to the
                  contrary, neither Basin nor any of its Affiliates or
                  Associates shall be deemed to be an Acquiring Person solely by
                  virtue of (i) the announcement of the Merger (as such term is
                  defined in the Merger Agreement), (ii) the acquisition of
                  Common Shares of the Company pursuant to the Merger, (iii) the
                  execution of the Merger Agreement, the Company Voting
                  Agreement or the Basin Voting Agreement or (iv) the
                  consummation of the Merger or of the other transactions
                  contemplated in the Merger Agreement, the Company Voting
                  Agreement or the Basin Voting Agreement."

                  (c) The following definitions shall be added to Section 1 of
the Rights Agreement:

                  ""Basin" shall mean Basin Exploration, Inc., a Delaware
corporation."

                  ""Basin Voting Agreement" shall mean the Voting Agreement
among the Company, Basin and the Basin stockholders signatory thereto dated the
date hereof."

                  ""Company Sub" shall mean Partner Acquisition Corp., a
Delaware corporation."

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                  ""Company Voting Agreement" shall mean the Voting Agreement
among the Company, Basin and the Company stockholders signatory thereto dated
the date hereof."

                  ""Merger Agreement" shall mean the Agreement and Plan of
Merger among the Company, Basin and the Company Sub dated the date hereof, as
such agreement may be amended from time to time."

                  ""Merger Documents" shall mean the Merger Agreement, the
Company Voting Agreement and the Basin Voting Agreement."

                  ""Merger Transactions" shall mean the transactions
contemplated under the Merger Documents."

                  (d) Section 3(a) of the Rights Agreement is amended to add the
following sentence at the end thereof:

                  "Notwithstanding anything in this Rights Agreement to the
                  contrary, a Distribution Date or a Shares Acquisition Date
                  shall not be deemed to have occurred solely as the result of
                  (i) the announcement of the Merger, (ii) the acquisition of
                  Common Shares of the Company pursuant to the Merger, (iii) the
                  execution of the Merger Agreement, the Company Voting
                  Agreement or the Basin Voting Agreement or (iv) the
                  consummation of the Merger or of the other transactions
                  contemplated in the Merger Agreement, the Company Voting
                  Agreement or the Basin Voting Agreement."

                  Section 2. Full Force and Effect. Except as expressly amended
hereby, the Rights Agreement shall continue in full force and effect in
accordance with the provisions thereof on the date hereof.

                  Section 3. Governing Law. This Amendment shall be governed by
and construed in accordance with the laws of the State of Delaware applicable to
contracts to be made and performed entirely within such State; provided,
however, that any provision regarding the rights, duties and obligations of the
Rights Agent shall be governed by and construed in accordance with the laws of
the State of New York applicable to contracts made and to be performed entirely
within such State.

                  Section 4. Severability. If any term, provision, covenant or
restriction of this Amendment is held by a court of competent jurisdiction or
other authority to be invalid, void or unenforceable, the remainder of the
terms, provisions, covenants and restrictions of this Amendment shall remain in
full force and effect and shall in no way be affected, impaired or invalidated.

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                  IN WITNESS WHEREOF, the Company and the Rights Agent have
caused this Amendment to be duly executed as of the day and year first above
written.



                                       STONE ENERGY CORPORATION

                                       by: /s/ Andrew L. Gates, III
                                          ------------------------
                                          Name:  Andrew L. Gates, III
                                          Title:  Vice President and
                                                  General Counsel



                                      CHASEMELLON
                                      SHAREHOLDER SERVICES, L.L.C., as
                                      Rights Agent

                                      by: /s/ David M. Cary
                                         -----------------
                                         Name:  David M. Cary
                                         Title:  Assistant Vice President