<PAGE>   1

                                                                     EXHIBIT 4.6



                  COMPANY VOTING AGREEMENT (this "Agreement") dated as of
         October 28, 2000, among Stone Energy Corporation, a Delaware
         corporation ("Partner"), Basin Exploration, Inc., a Delaware
         corporation ("Company"), and the other parties signatory hereto (each a
         "Stockholder").

         WHEREAS, each Stockholder desires that Company, Partner and Partner
Acquisition Corp., a Delaware corporation and wholly-owned subsidiary of Partner
("Merger Sub"), enter into an Agreement and Plan of Merger dated the date hereof
(as the same may be amended or supplemented, the "Merger Agreement"; capitalized
terms used but not defined herein shall have the meanings set forth in the
Merger Agreement) providing for the merger of Merger Sub with and into Company
(the "Merger") upon the terms and subject to the conditions set forth in the
Merger Agreement; and

         WHEREAS, each Stockholder and Company are executing this Agreement as
an inducement to Partner to enter into and execute, and to cause Merger Sub to
enter into and execute, the Merger Agreement;

         NOW, THEREFORE, in consideration of the execution and delivery by
Partner and Merger Sub of the Merger Agreement and the mutual covenants,
conditions and agreements contained herein and therein, the parties agree as
follows:

         1. Representations and Warranties. (a) Each Stockholder severally
represents and warrants to Partner as follows:

            (i) Such Stockholder is the record and beneficial owner of, or is
         the sole trustee of a trust that is the record holder of, and whose
         beneficiaries are the beneficial owners of, the number of shares of
         common stock, par value $0.01 per share, of Company (the "Common
         Stock") set forth opposite such Stockholder's name on Schedule A hereto
         (such shares of Common Stock, together with any other shares of Common
         Stock or other capital stock of Company acquired after the date hereof
         (including through the exercise of any stock options, warrants or
         similar instruments) being collectively referred to herein as the
         "Subject Shares"). The Subject Shares constitute the only shares, with
         respect to which such Stockholder is the record or beneficial owner, of
         Common Stock, preferred stock or other capital stock of Company or
         options, warrants or other rights (whether or not contingent) to
         acquire such shares of capital stock of Company that are or may be
         entitled to vote on the Merger or the Merger Agreement at any meeting
         of stockholders of Company called to vote upon the Merger or the Merger
         Agreement. Such Stockholder has the sole right to vote and Transfer (as
         defined below in Section 3(a)) the Subject Shares set forth opposite
         its name on Schedule A hereto, and none of such Subject Shares is
         subject to any voting trust or other agreement, arrangement or
         restriction with respect to the voting or the Transfer of the Subject
         Shares, except as provided by this Agreement (it being understood that
         any pledge of the Pledged Shares (as defined below) shall not be a
         breach of this representation). Such Stockholder has all requisite
         power and authority, and, if such Stockholder is a natural person, the
         legal capacity, to enter into this Agreement and to perform its
         obligations hereunder. To the extent that such Stockholder is an entity
         and not an individual, such Stockholder is duly organized, validly
         existing and in good standing under the laws of its jurisdiction of
         organization. The execution and delivery of this Agreement by such

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         Stockholder and the performance by such Stockholder of its obligations
         hereunder have been duly authorized by all necessary action on the part
         of such Stockholder. This Agreement has been duly executed and
         delivered by, and constitutes a valid and binding agreement of, such
         Stockholder, enforceable against such Stockholder in accordance with
         its terms, except as enforcement may be limited by bankruptcy,
         insolvency, moratorium or other similar laws and except that the
         availability of equitable remedies, including specific performance, is
         subject to the discretion of the court before which any proceeding for
         such remedy may be brought (collectively, the "Bankruptcy and Equity
         Exceptions").

            (ii) Neither the execution and delivery of this Agreement nor the
         performance by such Stockholder of its obligations hereunder will
         result in a violation of, or a default under, or conflict with, (A) if
         such Stockholder is an entity, any provision of its certificate of
         incorporation, bylaws, partnership agreement, limited liability company
         agreement or similar organizational documents, (B) any contract, trust,
         commitment, agreement, understanding, arrangement or restriction of any
         kind (other than as may relate to the Pledged Shares but subject to the
         proviso set forth in (iv) below) to which such Stockholder is a party
         or bound or to which the Subject Shares are subject, except, in the
         case of clause (B) above, as would not prevent, delay or otherwise
         materially impair such Stockholder's ability to perform its obligations
         hereunder. Execution, delivery and performance of this Agreement by
         such Stockholder will not reasonably be expected to violate, or require
         any consent, approval or notice under, any provision of any judgment,
         order, decree, statute, law, rule or regulation applicable to such
         Stockholder or the Subject Shares, except (x) for any necessary filing
         under the Hart-Scott-Rodino Antitrust Improvements Act of 1976, (y) for
         any reports under Sections 13(d) and 16 of the Exchange Act as may be
         required in connection with this Agreement and the transactions
         contemplated hereby or (z) as would not reasonably be expected to
         prevent, delay or otherwise materially impair such Stockholder's
         ability to perform its obligations hereunder.

            (iii) If the Stockholder is married and the Subject Shares of the
         Stockholder constitute community property or spousal approval is
         otherwise required for this Agreement to be legal, valid and binding,
         then, to the extent so required, this Agreement has been duly
         authorized, executed and delivered by, and constitutes a valid and
         binding agreement of, the Stockholder's spouse, enforceable against
         such spouse in accordance with its terms, subject to the Bankruptcy and
         Equity Exceptions. Except for any consents duly obtained as of the date
         hereof and which will remain in full force and effect at such time or
         times as may be necessary to duly consent to such Stockholder's
         performance of its obligations hereunder, no trust of which such
         Stockholder is a trustee requires the consent of any beneficiary to the
         execution and delivery of this Agreement or to the performance by such
         Stockholder of its obligations hereunder.

            (iv) The Subject Shares and the certificates representing such
         Shares are held by such Stockholder, or by a nominee or custodian for
         the benefit of such Stockholder, free and clear of all liens, claims,
         security interests, proxies, voting trusts or agreements,
         understandings or arrangements or any other encumbrances whatsoever,
         except for (A) any such encumbrances or proxies arising hereunder or
         under the existing terms of a trust of which such Stockholder is the
         trustee or (B) any such encumbrances arising pursuant to the pledge of
         any Subject Shares by such Stockholder prior to the date hereof to a
         financial


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         institution or a brokerage firm (the "Pledged Shares"); provided,
         however, that such Stockholder represents that any such arrangement
         regarding such Pledged Shares shall not prevent, delay or otherwise
         materially impair such Stockholder's ability to execute and deliver
         this Agreement or perform its obligations hereunder and such
         Stockholder shall use his reasonable efforts to obtain an
         acknowledgment by the pledgee of the terms of this Agreement and such
         pledgee's agreement to execute a proxy or to otherwise vote the Pledged
         Shares (if and to the extent the voting power of the Pledged Shares is
         being or to be exercised by pledgee) in accordance with Section 2
         hereof.

            (v) No broker, investment banker, financial advisor or other person
         is entitled to any broker's, finder's, financial advisor's or other
         similar fee or commission based upon arrangements made by or on behalf
         of such Stockholder in connection with its entering into this
         Agreement.

            (vi) Such Stockholder understands and acknowledges that Partner is
         entering into, and causing Merger Sub to enter into, the Merger
         Agreement in reliance upon such Stockholder's execution and delivery of
         this Agreement.

         (b) Partner represents and warrants to each Stockholder that the
execution and delivery of this Agreement by Partner and the consummation by
Partner of the transactions contemplated hereby have been duly authorized by all
necessary action on the part of Partner.

         2. Voting Agreements. Each Stockholder severally agrees with, and
covenants to, Partner that, during the Term (as defined below) of this
Agreement, at any meeting of stockholders of Company called to vote upon the
Merger and the Merger Agreement or at any adjournment thereof or in any other
circumstances upon which a vote, consent or other approval (including by written
consent) with respect to the Merger and the Merger Agreement is sought, such
Stockholder shall, including by executing a written consent solicitation if
requested by Partner, vote (or cause to be voted) the Subject Shares in favor of
the Merger, the adoption by Company of the Merger Agreement and the approval of
the terms thereof and each of the other transactions expressly contemplated by
the Merger Agreement.

         3. Other Covenants. Each Stockholder severally agrees with, and
covenants to, Partner during the Term of this Agreement as follows:

         (a) Such Stockholder shall not after the date hereof (i) sell,
transfer, pledge, assign or otherwise dispose of (including by gift)
(collectively, "Transfer"), or consent to any Transfer of, any Subject Shares or
any interest therein, except pursuant to the Merger, (ii) enter into any
contract, option or other agreement with respect to any Transfer of any or all
of the Subject Shares or any interest therein, (iii) grant any proxy,
power-of-attorney or other authorization in or with respect to the Subject
Shares, except for this Agreement or (iv) deposit the Subject Shares into a
voting trust or enter into a voting agreement or voting arrangement with respect
to the Subject Shares; provided, that any such Stockholder may (x) Transfer any
of the Subject Shares to any other Stockholder who is on the date hereof a party
to this Agreement, or to any other person or entity that, prior to or coincident
with such Transfer, executes an irrevocable proxy to vote such Subject Shares in
accordance with Section 2 and (y) Transfer a de minimus amount of such Subject
Shares (which in the case of Mr. Michael Smith, shall include Transfers up to
75,000 shares in the aggregate);


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provided, however, that such Stockholder shall not transfer any Subject Shares
pursuant to the preceding proviso (i) without Partner's prior written consent,
not to be unreasonably withheld or delayed and (ii) if any such transfer, either
alone or in the aggregate with other transfers by Stockholders and other persons
who may be affiliates of Company, would preclude Partner's ability to account
for the business combination to be effected by the Merger as a pooling of
interests; provided, further the foregoing restrictions shall not be deemed
violated in the event of any action taken by the pledgee of any Pledged Shares
pursuant to the terms of any agreements existing as of the date hereof with
respect thereto so long as such Stockholder uses his reasonable efforts to
obtain an acknowledgment by the pledgee of the terms of this Agreement and such
pledgee's agreement to execute a proxy or to otherwise vote the Pledged Shares
(if and to the extent the voting power of the Pledged Shares is being or to be
exercised by pledgee) in accordance with Section 2 hereof; provided, further,
that the restrictions in this Section 3 shall not be deemed violated by any
Transfer of Subject Shares pursuant to a cashless exercise of stock options.

         (b) Such Stockholder hereby waives any rights of appraisal, or rights
to dissent from the Merger, that such Stockholder may have.

         (c) Such Stockholder shall not take any action prohibited by Section
6.01 of the Merger Agreement.

         4. Certain Events. Each Stockholder agrees that this Agreement and the
obligations hereunder shall attach to such Stockholder's Subject Shares and
shall be binding upon any person or entity to which legal or beneficial
ownership of such Shares shall pass, whether by operation of law or otherwise,
including without limitation such Stockholder's heirs, guardians, administrators
or successors. In the event of any stock split, stock dividend, merger,
reorganization, recapitalization or other change in the capital structure of
Company affecting the Common Stock, preferred stock or the acquisition of
additional shares of Common Stock, preferred stock or other voting securities of
Company by any Stockholder, the number of Shares listed on Schedule A beside the
name of such Stockholder shall be adjusted appropriately and this Agreement and
the obligations hereunder shall attach to any additional shares of Common Stock,
preferred stock or other voting securities of Company issued to or acquired by
such Stockholder.

         5. Stop Transfer. Company agrees with, and covenants to, Partner that
Company shall not register the transfer of any certificate representing any
Subject Shares, unless such transfer is made to Partner or Merger Sub or
otherwise in compliance with this Agreement.

         6. Stockholder Capacity. No person executing this Agreement who is or
becomes during the term hereof a director of Company makes any agreement or
understanding herein in his or her capacity as such director. Each Stockholder
signs solely in his or her capacity as the record and beneficial owner of, or
the trustee of a trust whose beneficiaries are the beneficial owners of, such
Stockholder's Subject Shares.

         7. Further Assurances. Each Stockholder shall, upon request of Partner,
execute and deliver any additional documents and take such further actions as
may reasonably be deemed by Partner to be necessary or desirable to carry out
the provisions hereof.

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         8. Termination. This Agreement, and all rights and obligations of the
parties hereunder, shall terminate upon (and shall only be effective from the
date hereof until) the first to occur of (the "Term") (i) the Effective Time of
the Merger or (ii) the date upon which the Merger Agreement is terminated in
accordance with its terms; provided, however, that (x) Section 9 shall survive
any termination of this Agreement and (y) termination of this Agreement pursuant
to Clause (ii) above shall not relieve any party hereto from liability for any
willful and knowing breach hereof prior to such termination.

         9. Miscellaneous.

         (a) All notices, requests, claims, demands and other communications
under this Agreement shall be in writing and shall be deemed given if delivered
personally or sent by overnight courier (providing proof of delivery) to the
parties at the following addresses (or at such other address for a party as
shall be specified by like notice): (i) if to Partner or Company, to the
appropriate address set forth in Section 9.02 of the Merger Agreement; and (ii)
if to a Stockholder, to the appropriate address set forth on Schedule A hereto.

         (b) The headings contained in this Agreement are for reference purposes
only and shall not affect in any way the meaning or interpretation of this
Agreement.

         (c) This Agreement may be executed in two or more counterparts, all of
which shall be considered one and the same agreement and shall become effective
as to any Stockholder when one or more counterparts have been signed by each of
Partner, Company and such Stockholder and delivered to Partner, Company and such
Stockholder.

         (d) This Agreement (including the documents and instruments referred to
herein) constitutes the entire agreement, and supersedes all prior agreements
and understandings, both written and oral, among the parties with respect to the
subject matter hereof, and this Agreement is not intended to confer upon any
other person (other than Merger Sub) any rights or remedies hereunder.

         (e) This Agreement shall be governed by, and construed in accordance
with, the laws of the State of Delaware, regardless of the laws that might
otherwise govern under applicable principles of conflicts of laws thereof.

         (f) Neither this Agreement nor any of the rights, interests or
obligations under this Agreement shall be assigned, in whole or in part, by
operation of law or otherwise, by any of the parties without the prior written
consent of the other parties, except by laws of descent or as expressly provided
by Section 3(a). Any assignment in violation of the foregoing shall be void.

         (g) As between any Stockholder and Company, each of such parties agrees
that irreparable damage to the other, non-breaching party would occur and that
such non-breaching party would not have any adequate remedy at law in the event
that any of the provisions of this Agreement were not performed in accordance
with their specific terms or were otherwise breached. It is accordingly agreed
that the non-breaching party shall be entitled to an injunction or injunctions
to prevent breaches by the other party of this Agreement and to enforce
specifically the terms and provisions of this Agreement in any Federal court
located in the State of Delaware or in any Delaware state court, this being in
addition to any other remedy to which it may be entitled at law

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or in equity. In addition, each of the parties hereto (i) consents to submit
such party to the personal jurisdiction of any Federal court located in the
State of Delaware or any Delaware state court in the event any dispute arises
out of this Agreement or any of the transactions contemplated hereby and (ii)
agrees that such party will not attempt to deny or defeat such personal
jurisdiction by motion or other request for leave from any such court.

         (h) If any term, provision, covenant or restriction herein, or the
application thereof to any circumstance, shall, to any extent, be held by a
court of competent jurisdiction to be invalid, void or unenforceable, the
remainder of the terms, provisions, covenants and restrictions herein and the
application thereof to any other circumstances shall remain in full force and
effect, shall not in any way be affected, impaired or invalidated, and shall be
enforced to the fullest extent permitted by law.

         (i) No amendment, modification or waiver in respect of this Agreement
shall be effective against any party unless it shall be in writing and signed by
such party.






                [Remainder of this page intentionally left blank]



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         IN WITNESS WHEREOF, Stone Energy Corporation, Basin Exploration, Inc.
and the Stockholders party hereto have caused this Agreement to be duly executed
and delivered as of the date first written above.

                                       STONE ENERGY CORPORATION


                                       By:   /s/ D. Peter Canty
                                          --------------------------------------
                                          Name:  D. Peter Canty
                                          Title: President and Chief
                                                 Operating Officer


                                       BASIN EXPLORATION, INC.


                                       By:   /s/ Michael S. Smith
                                          --------------------------------------
                                          Name:  Michael S. Smith
                                          Title: President and Chief Executive
                                                 Officer


                                       /s/   Michael S. Smith
                                       -----------------------------------------
                                       Name:   Michael S. Smith


                                       /s/   Neil L. Stenbuck
                                       -----------------------------------------
                                       Name:   Neil L. Stenbuck


                                       /s/   Howard L. Boigon
                                       -----------------------------------------
                                       Name:   Howard L. Boigon


                                       /s/   Donald H. Anderson
                                       -----------------------------------------
                                       Name:   Donald H. Anderson


                                       /s/   John F. Greene
                                       -----------------------------------------
                                       Name:   John F. Greene


                                       /s/   J. Paul Hellstrom
                                       -----------------------------------------
                                       Name:   J. Paul Hellstrom


                                       /s/   Michael A. Nicolais
                                       -----------------------------------------
                                       Name:   Michael A. Nicolais


                                       /s/   Larry D. Unruh
                                       -----------------------------------------
                                       Name:   Larry D. Unruh


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                                   SCHEDULE A


<TABLE>
<CAPTION>
                                                                                                Number of
                                                                Class of      Nature of         currently
Name                          Address                           stock         ownership         owned shares(1)
----                          -------                           ---------     ---------         --------------
<S>                           <C>                               <C>           <C>               <C>
Howard L. Boigon              2001 Ivy Street                   common        direct                26,199
                              Denver, CO 80207

Michael S. Smith              2 Sedgwick Drive                  common        direct             2,163,665
                              Englewood, CO 80110                             by trust              48,000
                                                                              by trust              48,000
                                                                              by spouse            304,300
                                                                              by daughter            2,000
                                                                              by daughter            2,000

Neil L. Stenbuck              805 13th Street                   common        direct                61,038
                              Boulder, CO 80302

Donald H. Anderson            370 17th St., Suite 2750          common        direct                 3,000
                              Denver, CO 80202

John F. Greene                P.O. Box 2168                     common        direct                34,000
                              Silverthorne, CO 80498

John Paul Hellstrom           75 Overlook Road                  common        direct                 2,190
                              Morristown, NJ 07960

Michael A. Nicolais           40 East 52nd St. - 9th FL         common        direct                11,000
                              New York, NY 10022

Larry D. Unruh                717 17th St., Suite 1600          common        direct                 1,000
                              Denver CO, 80202

</TABLE>

----------------
(1) Total does not include any options currently held by any such individuals.


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