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                                                                    EXHIBIT 99.2

                             BASIN EXPLORATION, INC.
                      PROXY SOLICITED BY BOARD OF DIRECTORS
                       FOR SPECIAL MEETING OF STOCKHOLDERS
                                February 1, 2001

     The undersigned stockholder of Basin Exploration, Inc., a Delaware
corporation (the "Company"), hereby revokes all previous proxies with respect to
the matters set forth herein and appoints Michael S. Smith and Howard L. Boigon,
or either of them, attorneys, agents and proxies of the undersigned, with full
power of substitution to each of them, to vote all the shares of common stock,
par value $0.01 per share, of the Company which are entitled to one vote per
share and which the undersigned may be entitled to vote at the special meeting
of stockholders of the Company to be held at the Brown Palace Hotel, Onyx Room,
321 17th Street, Denver, Colorado 80202, on February 1, 2001, at 9:00 a.m.,
M.S.T., and at any adjournment of such meeting, with all powers which the
undersigned would possess if personally present:

     1.   To approve the merger agreement dated as of October 28, 2000, among
          Stone Energy Corporation, Partner Acquisition Corp., which is a
          newly-formed subsidiary of Stone Energy Corporation, and Basin
          Exploration, Inc., and the transactions contemplated by the merger
          agreement, including the merger; and

     2.   To vote upon such other matters as may be properly brought before the
          meeting or any adjournment thereof.

     If no directions are given, the individuals designated above will vote for
     the above proposals and, at their discretion, on any other matter that may
     come before the meeting.

     The undersigned acknowledges receipt of the Notice of Special Meeting of
     Stockholders and the Joint Proxy Statement/Prospectus.

          (CONTINUED AND TO BE VOTED, DATED AND SIGNED ON REVERSE SIDE)
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                             BASIN EXPLORATION, INC.
                    COMMON STOCK PROXY ONE (1) VOTE PER SHARE
                          PLEASE MARK VOTES [-] OR [X]

THE BOARD OF DIRECTORS RECOMMENDS A VOTE FOR THE FOLLOWING PROPOSAL:

THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS

     No. 1. To approve the Agreement and Plan of Merger, dated as of October 28,
2000, among Stone Energy Corporation, Partner Acquisition Corp., a wholly-owned
subsidiary of Stone, and Basin, and the transactions contemplated thereby,
including the merger, pursuant to which Partner Acquisition Corp. will be merged
with and into Basin and each share of common stock, $0.01 par value per share,
of Basin issued and outstanding immediately prior to the merger (other than
shares held by Stone, Basin or their respective subsidiaries, which will be
canceled) will be converted into the right to receive .3974 of a share of common
stock, $0.01 par value, of Stone.

         [ ] FOR                 [ ] AGAINST             [ ] ABSTAIN

     All other matters that may come before the meeting.

      [TELEPHONE PICTURE] VOTE BY TELEPHONE OR INTERNET [COMPUTER PICTURE]
                          QUICK *** EASY *** IMMEDIATE

YOUR VOTE IS IMPORTANT!--YOU CAN VOTE IN ONE OF THREE WAYS:

1.   TO VOTE BY PHONE: Call toll-free 1-800-840-1208 on a touch tone telephone
     24 HOURS A DAY-7 DAYS A WEEK

    There is NO CHARGE to you for this call.--HAVE YOUR PROXY CARD IN HAND.
        You will be asked to enter a Control Number, which is located in
              the box on the lower right hand corner of this form

     To vote as the board of directors of Basin recommends on the proposal,
     press 1; AGAINST, press 9; ABSTAIN, press 0.

                    WHEN ASKED, PLEASE CONFIRM BY PRESSING 1.

                                       OR

2.   TO VOTE BY INTERNET: Follow the instructions at our Website Address:
     http://www.eproxy.com/

                                       OR

3.   TO VOTE BY PROXY CARD: Mark, sign and date your proxy card and return
     promptly in the enclosed envelope.

NOTE: IF YOU VOTE BY INTERNET OR TELEPHONE, THERE IS NO NEED TO MAIL BACK YOUR
PROXY CARD; IF YOU DO NOT VOTE BY INTERNET OR TELEPHONE, PLEASE COMPLETE, SIGN
AND PROMPTLY MAIL THIS PROXY IN THE ENCLOSED ENVELOPE.

Signature                                             Dated:
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NOTE: Stockholder(s) should sign above exactly as name(s) appears hereon. But
minor discrepancies in such signatures shall not invalidate their proxy. If more
than one stockholder, all should sign.

      Please date, sign and mail your proxy card back as soon as possible!

                              THANK YOU FOR VOTING