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                                UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549

                                 SCHEDULE 14A

          Proxy Statement Pursuant to Section 14(a) of the Securities
                    Exchange Act of 1934 (Amendment No.  )

Filed by the Registrant [X]

Filed by a Party other than the Registrant [_]

Check the appropriate box:

[_]  Preliminary Proxy Statement

[_]  CONFIDENTIAL, FOR USE OF THE
     COMMISSION ONLY (AS PERMITTED BY
     RULE 14A-6(E)(2))

[_]  Definitive Proxy Statement

[X]  Definitive Additional Materials

[_]  Soliciting Material Pursuant to (S) 240.14a-11(c) or (S) 240.14a-12


                        BELLWETHER EXPLORATION COMPANY
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               (Name of Registrant as Specified In Its Charter)


- --------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if other than the Registrant)


Payment of Filing Fee (Check the appropriate box):

[X]  No fee required.

[_]  Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.


     (1) Title of each class of securities to which transaction applies:

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     (2) Aggregate number of securities to which transaction applies:

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     (3) Per unit price or other underlying value of transaction computed
         pursuant to Exchange Act Rule 0-11 (set forth the amount on which
         the filing fee is calculated and state how it was determined):

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     (4) Proposed maximum aggregate value of transaction:

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     (5) Total fee paid:

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[_]  Fee paid previously with preliminary materials.

[_]  Check box if any part of the fee is offset as provided by Exchange
     Act Rule 0-11(a)(2) and identify the filing for which the offsetting fee
     was paid previously. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.

     (1) Amount Previously Paid:

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     (2) Form, Schedule or Registration Statement No.:

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     (3) Filing Party:

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     (4) Date Filed:

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Notes:


                         BELLWETHER EXPLORATION COMPANY
                         1331 Lamar Street, Suite 1455
                           Houston, Texas  77010-3039
                                 (713) 650-1025

                    NOTICE OF ANNUAL MEETING OF STOCKHOLDERS
                       TO BE HELD WEDNESDAY, MAY 31, 2000

To the Stockholders of
   Bellwether Exploration Company:

     After printing the Proxy Statement for the 2000 Annual Meeting of
Stockholders of Bellwether Exploration Company (the "Company"), the Company
learned that the Annual Report to stockholders for the period ending December
31, 1999 would not be printed in time for mailing to stockholders on May 3,
2000.  In order to ensure that stockholders receive sufficient notice and have
time to review the Annual Report, THE DATE OF THE ANNUAL MEETING OF STOCKHOLDERS
OF THE COMPANY HAS BEEN CHANGED FROM FRIDAY, MAY 19, 2000 TO WEDNESDAY, MAY 31,
2000 (the "Annual Meeting").

     The Annual Meeting will be held on Wednesday, May 31, 2000, at the Houston
Center Club, 1100 Caroline Street, Houston, Texas at 10:00 a.m., Houston time,
for the following purposes:

     1.   To elect the nominees to the Board of Directors to serve until their
          successors are duly elected and qualified.
     2.   To consider and vote upon the proposed amendment to the Company's 1996
          Stock Incentive Plan.
     3.   To transact such other business as may properly come before the Annual
          Meeting or any adjournment(s) thereof.

     The Record Date for the Annual Meeting is April 10, 2000.  A Supplement to
the Proxy Statement  has been included with the Proxy Statement describing all
of the changes to the Proxy Statement resulting from the change of the date of
the Annual Meeting and postponement of the mailing date of the Proxy Statement
and Annual Report.

     THIS NOTICE OF ANNUAL MEETING OF STOCKHOLDERS SUPERCEDES IN ITS ENTIRETY
THE NOTICE OF ANNUAL MEETING OF STOCKHOLDERS DATED APRIL 28, 2000.

     You are cordially invited to attend the Annual Meeting.  The enclosed
proxy, which refers to the Annual Meeting to be held on May 19, 2000, will be
used for the Annual Meeting on May 31, 2000. Whether or not you are planning to
attend the Annual Meeting, you are urged to complete, date and sign the enclosed
proxy and return it promptly.

                                         Sincerely,

                                         /s/ J. P. Bryan

                                         J. P. Bryan
                                         Chairman of the Board and Chief
                                         Executive Officer
Houston, Texas
May 15,  2000


                          SUPPLEMENT TO PROXY STATEMENT

                             --------------------

                         BELLWETHER EXPLORATION COMPANY
                         1331 Lamar Street, Suite 1455
                           Houston, Texas 77010-3039
                                 (713) 650-1025


                         Annual Meeting of Stockholders
                            Wednesday, May 31, 2000

                                  INTRODUCTION

     This Supplement to the Proxy Statement dated April 28, 2000 is being
furnished in connection with the solicitation of proxies by and on behalf of the
Board of Directors of Bellwether Exploration Company (the "Company") for use at
the Annual Meeting of Stockholders of the Company to be held on Wednesday, May
31, 2000 (the "Annual Meeting") at 10:00 a.m., Houston time, at the Houston
Center Club, 1100 Caroline Street, Houston, Texas, and at any adjournment(s)
thereof, for the purposes set forth in this Proxy Statement.

     After printing the Proxy Statement for the 2000 Annual Meeting, the Company
learned that the Annual Report to stockholders for the period ending December
31, 1999 would not be printed in time for mailing to stockholders on May 3,
2000.  In order to ensure that stockholders receive sufficient notice and have
time to review the Annual Report, THE DATE OF THE ANNUAL MEETING OF STOCKHOLDERS
OF THE COMPANY HAS BEEN CHANGED FROM FRIDAY, MAY 19, 2000 TO WEDNESDAY, MAY 31,
2000.

     This Supplement to the Proxy Statement, the Proxy Statement and the
enclosed form of proxy are being mailed on or about May 15, 2000 to the
stockholders of record as of April 10,  2000 (the "Record Date").  The Annual
Report to stockholders for the year ended December 31, 1999 is also being mailed
to stockholders contemporaneously with this Proxy Statement, although the Annual
Report does not form a part of the materials for the solicitation of proxies.

PROXY

     The enclosed form of proxy references the Annual Meeting on May 19, 2000.
This proxy will be used for the Annual Meeting on May 31, 2000.

AMENDMENTS TO PROXY STATEMENT

     The section of the Proxy Statement entitled "Stockholders' Proposals for
2001 Annual Meeting" is amended and superceded in its entirety as follows.

                STOCKHOLDERS' PROPOSALS FOR 2001 ANNUAL MEETING

     No person other than nominees selected by the Board of Directors shall be
eligible for election as a director unless written notice of a nomination is
received from a stockholder of record by the Secretary of the Company not less
than 90 days prior to the 2001 Annual Meeting, accompanied by the written
consent of the nominee to be a nominee and to serve as a director.  Such
statement must


also contain the Company stock ownership of the nominee, occupations and
business history for the previous five years, other directorships and all other
information required by the federal proxy rules in effect at the time the
proposed nominee submits the statement.

     Proposals of stockholders of the Company that are intended to be presented
at the 2001 Annual Meeting of the Stockholders of the Company must be received
by the Secretary of the Company no later than January 15, 2001.  If the date of
the 2001 Annual Meeting of Stockholders is changed by more than 30 days from the
date of the 2000 Annual Meeting, the deadline for submitting proposals is a
reasonable time before the Company begins to print and mail its proxy materials
for its 2001 Annual Meeting.  Such proposals must be in conformity with all
applicable legal provisions including Rule 14a-8 of the General Rules and
Regulations under the Exchange Act and the Bylaws of the Company.

     The persons named in the Company's form of proxy for the 2001 Annual
Meeting will have discretionary authority to vote any proxies they hold at such
meeting on any matter for which the Company does not receive notice by March 31,
2001, unless the Company changes the date of its 2001 Annual Meeting of
Stockholders by more than 30 days from the date of the 2000 Annual Meeting, in
which case such person will be able to exercise discretionary authority if
notice of the matter has not been received in a reasonable time before the
Company mails its proxy materials for the 2001 Annual Meeting of Stockholders.

     If the date of the 2001 Annual Meeting of Stockholders is advanced or
delayed by more than 30 calendar days from the date of the 2000 Annual Meeting,
the Company shall, in a timely manner, inform stockholders of such change by
including a notice under Item 5, in its earliest possible quarterly report on
Form 10-Q.  The notice will include the new deadline for submitting proposals to
be included in the Company's proxy statement and the new date for determining
whether the Company may exercise discretionary voting authority because it has
not received timely notice of a matter.

     In order to avoid controversy as to the date on which any such proposal is
received by the Company, it is suggested that stockholders submit their
proposals by certified mail, return receipt requested, or other means that
permit them to prove the date of delivery.

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