BELLWETHER EXPLORATION CO
DEF 14A, 1999-04-23
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>
 
 
                           SCHEDULE 14A INFORMATION
Proxy Statement Pursuant to Section 14(a) of the Securities Exchange Act of 1934


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))

[X] Definitive Proxy Statement
 
[_] Definitive Additional Materials
 
[_] Soliciting Material Pursuant to (S) 240.14a-11(c) or  (S) 240.14a-12

                        BELLWETHER EXPLORATION COMPANY
               ------------------------------------------------
               (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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<PAGE>
 
                        [BELLWETHER LOGO APPEARS HERE]

                        BELLWETHER EXPLORATION COMPANY


                                 April 28, 1999

Dear Stockholder,

     You are cordially invited to attend the Annual Meeting of Stockholders of
Bellwether Exploration Company which will be held at the Houston Center Club,
1100 Caroline Street, Houston, Texas, on Friday, May 28, 1999, at 10:00 a.m.,
Houston time.

     The Notice of the Annual Meeting and Proxy Statement, which are attached,
provide information concerning the matters to be considered at the meeting.  The
report to stockholders for the period ending December 31, 1998 is being mailed
to stockholders along with these proxy materials.

     It is important that your shares be represented at this Annual Meeting,
regardless of the size of your holdings.  We urge you to return the signed proxy
in the enclosed envelope as soon as possible.  If you do attend the meeting in
person, you may withdraw your proxy and vote your stock if you so desire.  We
value your opinions and encourage you to participate in the Annual Meeting by
voting your proxy.

                                        Very truly yours,

                                        /s/ J. DARBY SERE
                                        ----------------------------------
                                        J. Darby Sere
                                        Chairman of the Board and
                                        Chief Executive Officer


1331 Lamar   Suite 1455  Houston, Texas  77010-3039    Phone: (713) 650-1025
                              Fax: (713) 652-2916
<PAGE>
 
                        BELLWETHER EXPLORATION COMPANY
                         1331 LAMAR STREET, SUITE 1455
                          HOUSTON, TEXAS  77010-3039
                                (713) 650-1025

                   NOTICE OF ANNUAL MEETING OF STOCKHOLDERS
                        TO BE HELD FRIDAY, MAY 28, 1999

To the Stockholders of
Bellwether Exploration Company:

     The Annual Meeting of Stockholders of BELLWETHER EXPLORATION COMPANY (the
"Company") will be held at the Houston Center Club, 1100 Caroline Street,
Houston, Texas at 10:00 a.m., Houston time, on Friday, May 28, 1999, 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 transact such other business as may properly come before the Annual
          Meeting or any adjournment(s) thereof.

     Stockholders of record at the close of business on April 13, 1999, are
entitled to notice of and to vote at the Annual Meeting and any adjournment(s)
thereof.  A complete list of all stockholders entitled to vote at the Annual
Meeting will be open for examination by any stockholder for any purpose germane
to the Annual Meeting, during normal business hours for a period of ten days
prior to the Annual Meeting, at the offices of the Company at 1331 Lamar Street,
Suite 1455, Houston, Texas 77010-3039.  Such list will also be available at the
Annual Meeting and may be inspected by any stockholder who is present for any
purpose germane to the Annual Meeting.

     You are cordially invited to attend the Annual Meeting.  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. DARBY SERE
                                     -------------------------------------      
                                     J. Darby Sere
                                     Chairman of the Board and Chief 
                                     Executive Officer


Houston, Texas
April 28, 1999



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

                            YOUR VOTE IS IMPORTANT
 
           TO ENSURE REPRESENTATION AT THE MEETING, PLEASE COMPLETE,
    DATE, SIGN AND PROMPTLY RETURN THE ENCLOSED PROXY IN THE ACCOMPANYING 
           POSTAGE-PAID ENVELOPE. NO ADDITIONAL POSTAGE IS NECESSARY
                        IF MAILED IN THE UNITED STATES.


- -------------------------------------------------------------------------------
<PAGE>
 
                                PROXY STATEMENT

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


                         ANNUAL MEETING OF STOCKHOLDERS
                              Friday, May 28, 1999

                                  INTRODUCTION

     This Proxy Statement 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 Friday, May 28, 1999 (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.

     This Proxy Statement and the enclosed form of proxy are being mailed on or
about April 28, 1999 to the stockholders of record as of April 13, 1999.  The
Annual Report to stockholders for the fiscal year ended December 31, 1998 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.

                 MATTERS TO BE CONSIDERED AT THE ANNUAL MEETING

     Unless otherwise indicated, proxies in the form enclosed that are properly
executed, duly returned and not revoked will be voted in favor of the election
of the seven nominees to the Board of Directors of the Company named herein.
The Board of Directors is not presently aware of other proposals which may be
brought before the Annual Meeting.  In the event other proposals are brought
before the Annual Meeting, the persons named in the enclosed form of proxy will
vote in accordance with what they consider to be in the best interests of the
Company and its stockholders.

                            QUORUM AND OTHER MATTERS

     The presence in person or by proxy of the holders of a majority of the
outstanding shares of Common Stock on the Record Date is necessary to constitute
a quorum at the Annual Meeting.  Shares of Common Stock represented by a
properly signed and returned proxy will be counted as present at the Annual
Meeting for purposes of determining a quorum, without regard to whether the
proxy is marked as casting a vote or abstaining.  Shares of Common Stock held by
nominees which are voted on at least one matter coming before the Annual Meeting
will also be counted as present for purposes of determining a quorum, even if
the beneficial owner has withheld from the nominee discretion (a "non-vote") for
voting on some or all other matters.

                              VOTING REQUIREMENTS

     The Board of Directors of the Company has fixed the close of business on
April 13, 1999, as the record date (the "Record Date") for the determination of
stockholders entitled to notice of and to vote at the Annual Meeting.  On the
Record Date, the Company had issued and outstanding 13,854,002 shares of its
common stock, $.01 par value ("Common Stock").  Only the record owners of the
Company's Common Stock on the Record Date are entitled to notice of and to vote
at the Annual Meeting.
<PAGE>
 
     Each share of Common Stock is entitled to one vote, in person or by proxy,
with respect to the election of directors and any other proposal properly
brought before the Annual Meeting.  The election of directors requires the
favorable vote of the holders of a plurality of shares of Common Stock present
and voting, in person or by proxy, at the Annual Meeting.  Abstentions and
broker non-votes have no effect on determinations of plurality except to the
extent that they affect the total votes received by any particular candidate.

     Votes at the Annual Meeting will be tabulated by an Inspector of Election
appointed by the Company.

                               PROXY INFORMATION

     A proxy in the form accompanying this Proxy Statement, when properly
executed and returned, will be voted in accordance with the directions specified
on the proxy, and otherwise in accordance with the judgment of the persons
designated therein as proxies.  Any proxy which does not withhold authority to
vote or on which no other instructions are given will be voted for the election
of the nominees named herein to the Board of Directors and in favor of the other
proposals set forth herein.

     The enclosed form of proxy may be revoked at any time prior to its exercise
by executing a new proxy with a later date, by voting in person at the Annual
Meeting, or by giving written notice of revocation to Robert J. Bensh, Secretary
of the Company, at any time before the proxy is voted at the Annual Meeting.
Please ensure that your shares will be voted by completing, signing, dating and
returning the enclosed form of proxy in the enclosed postage-paid envelope.

                                      -2-
<PAGE>
 
                       BENEFICIAL OWNERSHIP OF SECURITIES

Management and Principal Stockholders

     The following table sets forth, as of the Record Date, certain information
with respect to ownership of the Company's Common Stock as to (a) all persons
known to the Company to be the beneficial owners of more than five percent of
the outstanding shares of Common Stock, (b) each director, (c) each nominee for
director, (d) each of the executive officers named in the Summary Compensation
Table, and (e) all executive officers and directors of the Company as a group.
The information set forth in the following table is based on public filings made
with the Securities and Exchange Commission (the "Commission") as of the Record
Date and certain information supplied to the Company by the persons listed
below.  Unless otherwise indicated, all shares of Common Stock are owned
directly and each owner has sole voting and investment power with respect
thereto.


<TABLE>
<CAPTION>
                                                          Amount and Nature of 
       Name and Address of Beneficial Owner               Beneficial Ownership         Percent of Class
- ---------------------------------------------------     -----------------------        ----------------
<S>                                                        <C>                         <C>
Prudential Insurance Company of America............         1,417,400  (a)                    10.23%
 751 Broad Street                                       
 Newark, New Jersey  07102-3777                         
                                                        
Alpine Investment Partners.........................           979,832  (b)                     7.07%
Rho Management Trust III                                
 767 Fifth Avenue                                       
 New York, New York  10153                              
                                                        
Dimensional Fund Advisors Inc......................           847,000 (c)                      6.11%
 1299 Ocean Avenue, Eleventh Floor                                             
 Santa Monica, California  90401                                               
                                                                               
Fleet Financial Group, Inc.........................           729,299 (d)                      5.26%
 One Federal Street                                                            
 Boston, Massachusetts  02110                                                  
                                                                               
J. Darby Sere......................................           413,641 (e)                      2.93%
J. P. Bryan........................................           403,497 (f)                      2.86%
A. K. McLanahan....................................            22,250 (g)                       *
Vincent H. Buckley.................................            19,125 (g)                       *
Dr. Jack Birks.....................................            16,000 (g)                       *
Habib Kairouz......................................            18,000 (h)                       *
Townes G. Pressler.................................            11,500 (i)                       *
William C. Rankin..................................            78,000 (j)                       *
                                                        
All executive officers and directors as a group         
 (8 persons).......................................           982,013                          6.78%
</TABLE> 
- ---------------------------------------------------
* Under 1%

                                      -3-
<PAGE>
 
(a)  Based on a Schedule 13G/A filed with the Commission on February 9, 1999 by
     The Prudential Insurance Company of America ("Prudential").  Prudential has
     sole voting and investment power with respect to 362,400 shares of Common
     Stock and shared voting and investment power with respect to 1,055,000
     shares of Common Stock.

(b)  Based on a Schedule 13D/A filed with the Commission April 30, 1997, by Rho
     Management Partners, L.P. ("Rho"), Rho Management Trust III ("Trust"),
     Joshua Ruch, and Alpine Investment Partners ("Alpine").  Joshua Ruch and
     Rho may be deemed to be the beneficial owners of the shares of Common Stock
     held in the name of Alpine and the Trust.  Mr. Ruch and Rho share voting
     and dispositive power over 728,590 shares of Common Stock held in the name
     of Alpine and Mr. Ruch and the Trust share voting and dispositive power
     over 225,000 shares of Common Stock held in the name of the Trust.  Mr.
     Ruch also has sole voting and dispositive power over 26,242 of the shares
     shown.  The amount shown includes 1,242 shares beneficially owned by Mr.
     Ruch held in the name of XBF Inc.

(c)  Based on a Schedule 13G filed with the Commission on February 11, 1999 by
     Dimensional Fund Advisors Inc.

(d)  Based on a Schedule 13G filed with the Commission on February 13, 1998 by
     Fleet Financial Group, Inc. ("Fleet").  Fleet has sole voting power with
     respect to 623,399 shares of Common Stock, sole investment power with
     respect to 728,999 shares of Common Stock and shared investment power with
     respect to 300 shares of Common Stock.

(e)  Includes 257,000 shares of Common Stock that Mr. Sere has the right to
     acquire within 60 days pursuant to options and 4,400 shares of Common Stock
     owned by Mr. Sere's minor son.  Does not include 7,600 shares of Common
     Stock owned by Mr. Sere's wife, as to which Mr. Sere has no voting or
     dispositive power.

(f)  Includes 150,000 shares of Common Stock and a warrant to acquire 100,000
     shares of Common Stock beneficially owned by Torch Energy Advisors
     Incorporated ("Torch").  Mr. Bryan disclaims beneficial ownership of these
     shares.  Mr. Bryan is Senior Managing Director of and a holder of 120,920
     shares of Common Stock, representing a 23% ownership interest on a fully
     diluted basis, of the parent corporation of Torch.  Includes 141,000 shares
     of common stock which Mr. Bryan has the right to acquire within 60 days
     pursuant to options.  Excludes 6,250 shares of Common Stock owned by Mr.
     Bryan's wife, as to which he has no voting or dispositive power.

(g)  Includes 16,000 shares of Common Stock which the director has the right to
     acquire within 60 days pursuant to options.

(h)  Includes 18,000 shares of Common Stock which Mr. Kairouz has the right to
     acquire within 60 days pursuant to options.

(i)  Includes 8,000 shares of Common Stock which Mr. Pressler has the right to
     acquire within 60 days pursuant to options and 2,000 shares of Common Stock
     owned indirectly through Teepee Petroleum Company, Inc.

(j)  Includes 58,000 shares of Common Stock which Mr. Rankin has the right to
     acquire within 60 days pursuant to options.

                                      -4-
<PAGE>
 
                                   PROPOSAL I
                             ELECTION OF DIRECTORS

Nominees

      Each incumbent director identified in the table below is a nominee for
election as director of the Company.  The term of office for which the following
persons are nominated will expire at the time of the 2000 Annual Meeting of
Stockholders of the Company or when their respective successors shall have been
elected and qualified.  It is the intention of the persons named in the
accompanying proxy that proxies will be voted for the election of the seven
nominees named below unless otherwise indicated thereon.  Should any nominee for
the office of director named herein become unable or unwilling to accept
nomination or election, the person or persons acting under the proxies will vote
for the election in his stead such other person as the Board of Directors may
recommend.  The nominees have consented to be nominated and have expressed their
intention to serve if elected.  The Board of Directors has no reason to believe
that any of the nominees will be unable to serve if elected to office and, to
the knowledge of the Board of Directors, the nominees intend to serve the entire
term for which election is sought.  Only the nominees or substitute nominees
designated by the Board of Directors will be eligible to stand for election as
directors at the Annual Meeting.  See "Stockholders' Proposals for 2000 Annual
Meeting."

      Directors will be elected by a plurality vote of the shares of Common
Stock present, in person or by proxy, at the Annual Meeting.  The Board of
Directors recommends a vote FOR each of the nominees listed and, unless marked
to the contrary, proxies received from stockholders will be voted for the
election of such nominees.

Directors and Executive Officers

      The following table provides information with respect to the directors and
nominees for director and present executive officers of the Company.  Each
executive officer has been elected to serve until his successor is duly
appointed or elected by the Board of Directors or his earlier removal or
resignation from office.

<TABLE>
<CAPTION>
                                                        Company
               Name                      Age         Position Since        Present Company Position
- ----------------------------------     -------     -------------------     ------------------------
<S>                                       <C>            <C>                             <C>
J. Darby Sere                            51              1988               Chairman of the Board,* Chief
                                                                            Executive Officer, and President
William C. Rankin                        49              1997               Senior Vice President and Chief
                                                                            Financial Officer
Dr. Jack Birks                           79              1988               Director*
J. P. Bryan                              59              1987               Director*
Vincent H. Buckley                       76              1987               Director*
Habib Kairouz                            32              1994               Director*
A. K. McLanahan                          73              1987               Director*
Townes G. Pressler                       63              1998               Director*
</TABLE>
- ----------------------------------
*  Nominee for director


  Mr. Sere has been the Company's Chairman of the Board since June 2, 1997,
Chief Executive Officer since January 25, 1995, its President since November 27,
1997, and a Director since March 25, 

                                      -5-
<PAGE>
 
1988. Mr. Sere was the Company's Chief Executive Officer from March 7, 1988 to
June 29, 1994 and President from March 7, 1988 to June 2, 1997.

  Mr. Rankin has been Senior Vice President and Chief Financial Officer of the
Company since September 29, 1997.  Prior to joining the Company, Mr. Rankin was
Vice President and Chief Financial Officer of Gulfstar Energy, Inc.  From
February 1996 to March 1997, he was Senior Vice President and Chief Financial
Officer of Kelley Oil and Gas Corporation ("Kelley") and from March 1994 until
he joined Kelley, Vice President and Chief Financial Officer of Kelley's largest
shareholder, Contour Production Company.  From December 1985 to November 1993,
Mr. Rankin was a Financial Officer with Hadson Energy Resources Corporation and
its predecessors, serving the last four years as Senior Vice President, Chief
Financial Officer and a Director.

  Dr. Birks has been a Director of the Company since 1988.  He was Chairman of
the Board of Midland & Scottish Resources Plc. until September 30, 1997.  He is
life President of British Marine Technology Limited.  Dr. Birks served as
Chairman of the Board of North American Gas Investment Trust Plc. from 1989
until his retirement in 1995; as Chairman of the Board of Charterhouse Petroleum
Plc from 1982 to 1986; as Chairman of the Board of London American Energy Inc.
from 1982 to 1988; as Vice Chairman of the Board of Petrofina (UK) Limited from
1986 to 1989; and as a Managing Director of the Board of British Petroleum
Company Plc from 1978 until his retirement in March 1982.  He was appointed as a
Director of Gulf Indonesia Resources Limited in August 1997.

  Mr. Bryan has served as a Director of the Company since June 2, 1997.  He was
the Company's Chairman of the Board from August 31, 1987 to June 2, 1997, and
Chief Executive Officer from June 30, 1994 to January 25, 1995 and from August
31, 1987 to March 6, 1988.  From January 1995 to February 1998, Mr. Bryan was
Chief Executive Officer of Gulf Canada Resources Limited.  He was Chairman of
the Board of Nuevo Energy Company ("Nuevo") from March 1990 to December 1997,
and was Chief Executive Officer of Nuevo from March 1990 to January 1995.  Mr.
Bryan was also Chairman of the Board and Chief Executive Officer of Torch and
its predecessor from January 1985 to May 1997 and since October 1998 has served
as the Senior Managing Director of Torch.  Mr. Bryan is also a member of the
Board of Directors of Republic Waste Industries.

  Mr. Buckley has been a Director of the Company since 1987.  He has been Of
Counsel to the law firm of Locke, Liddell & Sapp, L.L.P. since January 1989.  He
also serves as a Director of Enron Cactus III Corporation, a Director of Enron
Cash Company and an Independent Manager of ECT Coal Co. III.  Mr. Buckley was
President and Chief Executive Officer of Cockburn Oil Corporation from August
1984 until September 1988, and was Vice President of Apache Corporation, an oil
and gas company, from October 1982 to August 1984.  From June 1950 until October
1982, he served in various legal and management positions for the Dow Chemical
Company.

  Mr. Kairouz has been a Director of the Company since August 26, 1994. Mr.
Kairouz is a Managing Director of Rho Management Company, Inc., an investment
advisory firm which serves as advisor to the principal investor of Alpine
Investment Partners. Prior to joining Rho in 1993, Mr. Kairouz was employed for
five years in investment banking at the firms of Jesup & Lamont Securities, Inc.
and more recently, Reich & Co., Inc. Under the agreement pursuant to which the
Company acquired Odyssey Petroleum Company, certain former owners ("Owners") of
the Odyssey Partnership acquired the right to designate one representative to
the Company's Board of Directors. Pursuant to such agreement, until the earlier
to occur of the five-year anniversary of the closing of such acquisition or the
date such Owners no longer own at least 5% of the outstanding Common Stock of
the Company, the Company is obligated to nominate and recommend to the Company's
stockholders one representative of the Owners. Mr. Kairouz is the person so
designated by the Owners.

  Mr. McLanahan has been a Director of the Company since November 6, 1987.  He
has been a First Vice President of PaineWebber Incorporated ("PaineWebber")
since January, 1995.  He was a Vice President of Kidder Peabody & Co., Inc., an
investment banking firm, from April 1985 until its sale to 

                                      -6-
<PAGE>
 
PaineWebber in 1995. From April 1982 to April 1985, he served as a Senior Vice
President and Branch Office Manager of Donaldson, Lufkin & Jenrette, Inc., an
investment banking firm. Mr. McLanahan currently serves as Chairman of the
Houston Symphony Society and the Governing Board of the Yale University Art
Gallery.

  Mr. Pressler has been a Director of the Company since May 22, 1998.  He has
been owner and President of Tepee Petroleum Company, Inc., an exploration and
production company with operations in Texas, Louisiana and Oklahoma, and
Pressler Petroleum Consultants, a reservoir engineering consulting firm, since
1985.  He currently serves as a Trustee of Pacific American Investors Trust and
as a Director of Korea Industrial Holdings, Ltd.  From 1983 to 1985, he was
President, Chief Operating Officer and Director of Philip Hill Energy, Inc., PHE
(Texas) Inc. and PHE (Ohio) Inc., three exploration and production companies
owned by Philip Hill Investment Trust, London.  From 1979 to 1983, he was co-
founder, President and Director of Republic Oil and Gas Corp., a private
exploration and production company.  Mr. Pressler is a registered professional
engineer in the state of Texas and has 38 years of experience in the oil and gas
industry.

  All officers and directors (including the nominees) of the Company are United
States citizens, except Dr. Birks who is a citizen of the United Kingdom.

                             EXECUTIVE COMPENSATION

Summary Compensation Table

  The following Summary Compensation Table details annual and long-term
compensation paid during the periods indicated to persons described below:

<TABLE>
<CAPTION>
                                                                                    Long Term
                                             Annual Compensation                   Compensation
                          -------------------------------------------------------  ------------
 Name and Principal                                             Other Annual        Number of      All Other
 Position                 Fiscal Year    Salary      Bonus     Compensation (1)      Options     Compensation
- ---------------------     -----------   --------   ---------   ----------------    ------------  ------------
<S>                       <C>           <C>        <C>          <C>               <C>             <C>
J. Darby Sere........        1998       $234,000    $100,800         --               54,000       $58,085(2)
Chairman of the              1997(3)     103,500      57,000         --               55,000        27,217(4)
 Board and Chief             1997        183,000     100,000         --               55,000        30,037(5)
 Executive Officer           1996        171,000      70,000         --                    0        12,596(6)
 
William C. Rankin....        1998        176,400      45,900         --               24,000        26,143(7)
Senior Vice                  1997(3)      44,818      14,000         --              100,000         3,596(8)
 President and Chief
 Financial Officer
- ---------------------
</TABLE>

(1)  None of the named executive officers received perquisites or other personal
     benefits, securities or property, the aggregate annual amount of which
     exceeded the lesser of $50,000 or 10% of the total annual salary and bonus
     reported for the named executive.

(2)  Includes $32,010 in matching and profit-sharing contributions under the
     Company's Simplified Employee Pension Plan and matching deferred
     compensation contributions under the Company's Deferred Compensation Plan;
     $18,626 in payment of life insurance premiums; and $7,449 in payment of
     disability insurance premiums.

(3)  Prior to July 1, 1997, the Company's fiscal year end was June 30 of each
     year.  Subsequent to a transition period from July 1, 1997 to December 31,
     1997 (the "Transition Period"), the Company changed its fiscal year end to
     December 31.  The compensation reflected herein represents compensation
     paid during the six-month Transition Period.

                                      -7-
<PAGE>
 
(4)  Includes $4,750 in matching and profit-sharing contributions under the
     Company's Simplified Employee Pension Plan; $18,623 in payment of life
     insurance premiums; and $3,844 in payment of disability insurance premiums.

(5)  Includes $7,500 in matching contributions under the Company's Simplified
     Employee Pension Plan; $18,693 in payment of life insurance premiums; and
     $3,844 in payment of disability insurance premiums.

(6)  Includes $7,500 in matching contributions under the Company's Simplified
     Employee Pension Plan; $1,252 in payment of life insurance premiums; and
     $3,844 in payment of disability insurance premiums.

(7)  Includes $21,259 in matching and profit-sharing contributions under the
     Company's Simplified Employee Pension Plan and matching deferred
     compensation contributions under the Company's Deferred Compensation Plan
     and $4,885 in payment of disability premiums.

(8)  Includes $3,596 in matching and profit-sharing contributions under the
     Company's Simplified Employee Pension Plan.

Executive Employment Contracts

      On June 1, 1998, the Company entered into a three-year employment contract
with J. Darby Sere to serve as the Company's President and Chief Executive
Officer. The agreement provides for a base salary of $228,000 per year subject
to increase at the discretion of the Compensation Committee. Mr. Sere is also
entitled to a discretionary bonus based upon performance (as determined by the
Compensation Committee), reimbursement for certain club membership fees, the use
of a Company car and standard insurance and medical benefits.

      The agreement is terminable by either party, but, in the event that Mr. 
Sere's employment is terminated by the Company for reasons other than "cause" 
or by Mr. Sere for "good reason," the Company is obligated to pay Mr. Sere a 
severance payment equal to one and one-half times, or, in the event such 
termination occurs within two years of a change in control, three times, the sum
of his highest annual salary and highest annual bonus paid during the last two 
years immediately preceding the date of termination. In addition, outstanding 
stock options and restricted stock will immediately vest. "Cause" is generally 
defined in the agreement as the failure of Mr. Sere to render services to the 
Company as provided in the agreement or the commission of fraud or other 
specified illegal acts. "Good reason" is defined generally as a material change 
in position or duties, a change in control of the Company, a reduction in salary
or other benefits, a required relocation or a material breach of the agreement 
by the Company. 

      On June 1, 1998, the Company entered into a two-year employment agreement 
with William C. Rankin to serve as the Company's Senior Vice President and Chief
Financial Officer. The terms of this employment agreement provide for a base 
salary of $174,000 per year subject to increase at the discretion of the 
Compensation Committee. Mr. Rankin is also entitled to a discretionary bonus 
based upon performance (as determined by the Compensation Committee), 
reimbursement for certain club membership fees, an automobile allowance and 
standard insurance and medical benefits.

      The agreement is terminable by either party, but, in the event that Mr. 
Rankin's employment is terminated by the Company for reasons others than "cause"
or by Mr. Rankin for "good reason," the Company is obligated to pay Mr. Rankin a
severance payment equal to the sum of, or, in the event such termination occurs 
within two years of a change in control, two times the sum of, his highest 
annual salary and highest annual bonus paid during the last two years 
immediately preceding the date of termination. In addition, outstanding stock 
options and restricted stock will immediately vest. "Cause" and "good reason" 
have the same meaning in Mr. Rankin's contract as in Mr. Sere's.

Option Grants in Last Fiscal Year

      The following table sets forth certain information concerning grants of
options to purchase Common Stock made during the last fiscal year to the
executive officers named in the Summary Compensation Table.

<TABLE>
<CAPTION>
                                      Number of        % of Total
                                      Securities         Options
                                      Underlying        Granted to          Per Share                            Grant Date
                                       Options         Employees in         Exercise         Expiration           Present 
           Name                        Granted         Fiscal Year           Price (a)          Date              Value (b)
       -------------                -------------     --------------      -------------     ------------        -----------
<S>                                <C>                <C>                 <C>                <C>                <C>
J. Darby Sere..............                54,000           18%                $6.250          10/05/08             $85,320
 
William C. Rankin..........                24,000            8%                 6.250          10/05/08             $37,920
</TABLE>

(a)  The exercise price is the average of high and low price of the Common Stock
     on the date of grant.

(b)  In accordance with the rules of the Securities and Exchange Commission,
     this column illustrates the gains that may exist for the respective options
     over a ten-year period using the Black-Scholes option pricing model.  This
     valuation model is hypothetical; the actual value, if any, depends on the
     excess of the market price of the shares over the exercise price on the
     date the option is exercised.  If the market price does not increase above
     the exercise price, compensation to the grantee will be zero.  The Black-
     Scholes option pricing model is a mathematical formula used for estimating
     option values that incorporates various assumptions.  The Grant Date
     Present Value set out in the column above is based on the following
     assumptions: (a) a ten-year option term; (b) 40% expected future annual
     stock volatility for the options; (c) a risk-free rate of return of 5 1/2%
     for the options granted; and (d) no expected dividend yield. The above
     model does not include any reduction in value for non-transferability,
     forfeiture or vesting of options.

Aggregated Option Exercises in Last Fiscal Year and Fiscal Year End Option
Values

       The following table sets forth certain information concerning the
exercise during the last fiscal year of options to purchase Common Stock by the
executive officers named in the Summary Compensation Table and the number and
value of unexercised options to purchase Common Stock held by such individuals
at December 31, 1998.  Also reported are the values for "in-the-money" options
which represent the positive spread between the exercise price of any such
existing stock options and the December 31, 1998 price of the Common Stock.  The
actual amount, if any, realized upon exercise of 

                                      -8-
<PAGE>
 
stock options will depend upon the market price of the Common Stock relative to
the exercise price per share of Common Stock at the time the stock option is
exercised. There is no assurance that the values of unexercised, "in-the-money"
stock options reflected in this table will be realized.

<TABLE>
<CAPTION>
                                                                                                                 
                                                                                 Unexercised Options at December 31, 1998      
                                                                 ------------------------------------------------------------------ 

                               Number of                                   Number of                          Value of
                                 Shares                              Underlying Securities                In-the-Money Options
                                Acquired           Value         -----------------------------     --------------------------------
        Name                  On Exercise         Realized         Exercisable   Unexercisable         Exercisable    Unexercisable
    ------------             -------------     -------------     -------------   -------------      --------------    -------------
<S>                          <C>                <C>               <C>             <C>               <C>                <C>         
J. Darby Sere........          109,451          $519,892             231,000          78,000              --               --      
 
William C. Rankin....               --                --              25,000          99,000              --               --
</TABLE>

Long-Term Incentive Plan Awards in Last Fiscal Year

      At this time, the Company does not have a long-term incentive plan for its
employees, other than the 1994 Stock Incentive Plan ("1994 Plan") and the 1996
Stock Incentive Plan ("1996 Plan").

1988 Plan

      In 1988, the Board of Directors adopted and stockholders approved the
Company's 1988 Non-Qualified Stock Option Plan.  The Company reserved 131,325
shares of Common Stock under the 1988 Plan and no further options will be
granted under the 1988 Plan.  Options under the 1988 Plan were granted by the
Compensation Committee to directors, executive officers or key employees of the
Company.  The exercise price of an option was 100% of the fair market value on
the date of the grant.  Options granted under the 1988 Plan were all exercised
by March 25, 1998, the expiration date of the 1988 Plan and options granted
pursuant thereto.

1994 Plan

      In 1994, the Board of Directors adopted and stockholders approved the
Bellwether Exploration Company 1994 Stock Incentive Plan.  The Company has
reserved 825,000 shares of Common Stock under the 1994 Plan. The Company has
issued options to purchase an aggregate of 822,500 shares of Common Stock under
the 1994 Plan.

      The 1994 Plan is administered by the Compensation Committee of the Board
of Directors.  The Compensation Committee has full power to select, from among
the persons eligible for awards, the individuals to whom awards are granted, to
make any combination of awards to any participant and to determine the specific
terms of each grant, subject to the provisions of the 1994 Plan.  The option
price per share of Common Stock deliverable upon the exercise of a stock option
is 100% of the fair market value of a share of Common Stock on the date the
stock option is granted.

      Directors, officers and key employees of the Company and officers and key
employees of Torch who render services to the Company under the Administrative
Services Agreement between the Company and Torch, dated January 1, 1994
("Administrative Services Agreement") are eligible to receive stock options or
performance shares under the 1994 Plan.

1996 Plan

      In 1996, the Board of Directors adopted and the stockholders approved the
Bellwether Exploration Company 1996 Stock Incentive Plan.  The Company initially
reserved 500,000 shares of Common Stock under the 1996 Plan and amended the plan
on November 21, 1997 reserving another 500,000 shares.  

                                      -9-
<PAGE>
 
Members of the Board of Directors who are not employed by the Company receive
annual automatic grants of stock options.

      As of April 13, 1999, the Company had 153,000 shares of Common Stock
available for grant under the 1996 Plan.

         INFORMATION CONCERNING THE OPERATION OF THE BOARD OF DIRECTORS

      The small size of the Company's Board of Directors lends itself to
frequent informal discussions of Company matters among its members.  The Board
of Directors met formally four times during the last fiscal year.

      The Company has a Compensation Committee comprised of Messrs. McLanahan
and Buckley and Dr. Birks (the "Compensation Committee"). The function of the
Compensation Committee is to administer the 1994 Plan and the 1996 Plan, to
establish the compensation of the Company's Chief Executive Officer and to
review the compensation of the other officers of the Company. The Compensation
Committee also meets to review Torch's performance under the Administrative
Services Agreement, which agreement may be terminated by the Compensation
Committee.  The Compensation Committee met two times during the last fiscal
year.

      The Company has an Audit Committee composed of Messrs. McLanahan and
Buckley and Dr. Birks (the "Audit Committee").  The primary function of the
Audit Committee is to review the annual audit of the Company's financial
statements with the Company's independent accountants.  In addition, the Audit
Committee approves other professional services provided by the accountants and
evaluates the independence of the accountants.  The Audit Committee also reviews
the scope and results of the Company's procedures for internal auditing, the
adequacy of the Company's system of internal accounting controls, and the
Company's disclosure policies and procedures.  The Audit Committee met once
during the last fiscal year.

      During the last fiscal year, all directors attended at least 75% of the
total number of meetings of the Board of Directors, and each committee member
attended at least 75% of the total number of meetings held by all Committees on
which he served.

      The Company does not have a nominating committee.

Compensation Committee Interlocks And Insider Participation

      The service of the members of the Company's Compensation Committee does
not create any corporate interlocks or insider participation between the
Compensation Committee and another entity.

Compensation of Directors

      Directors of the Company who are neither officers nor employees of the
Company ("Non-Employee Directors") received $5,000 per quarter during the fiscal
year ended December 31, 1998, and were reimbursed for reasonable expenses
incurred in attending such meetings. Each member of the Compensation and Audit
Committees also received $1,000 per meeting.  Directors who are officers or
employees of the Company received no additional compensation for services as
members of the Board of Directors.  The Company paid a total of $134,000 in
director fees for the last fiscal year.  Each Non-Employee Director receives an
annual grant of 4,000 options under the 1996 Plan.

                                      -10-
<PAGE>
 
Report Of The Compensation Committee On Executive Compensation

      The Compensation Committee is responsible for establishing policies
concerning the compensation of the Company's executive officers. The report of
the Compensation Committee describing the Company's compensation philosophy and
objectives is presented below.

Compensation Committee Report

      As members of the Compensation Committee, we are responsible for the
administration of the Company's 1994 Plan and the 1996 Plan. We also evaluate
compensation levels of management and review with the Board of Directors the
various factors affecting compensation of the Company's highest paid officers.
In addition, the Compensation Committee considers management succession and
related matters.

      The Compensation Committee continues to endorse the compensation policy of
the Company, which is that a substantial portion of the annual compensation of
each officer must be related to the performance of the Company, as well as the
particular contribution of each officer.  The Committee believes, however, that
services of outstanding value can be rendered in periods of financial or
operating stringency as well as during times of economic prosperity and that
profitability under prevailing business conditions must be taken into account.

      During fiscal 1997, the Compensation Committee adopted an Annual and Long-
Term Incentive Plan to establish guidelines for base compensation, incentive
bonuses and stock options with the assistance of KPMG LLP, who prepared an
Executive and Director Compensation Review in fiscal 1996.  Performance measures
and targets were established pursuant to the Plan.

      In evaluating the compensation of the Company's officers for the year
ended December 31, 1998, the Committee recognized that several of the Company's
performance measures and targets were not met.  The Committee believes, however,
that a significant factor in the Company's failure to meet targets set at the
beginning of 1998 was the decline in oil prices from $14.44 at December 31, 1997
to $9.24 at December 31, 1998, a market factor over which executives have no
control. For instance, for the year ended December 31, 1998, there was a
reduction in oil and gas reserves compared to year-end 1997, based in part on
price-related negative revisions.  In addition, while operating cash flows did
not meet set thresholds, if prices received during 1997 were applied to 1998
production, operating cash flows would have exceeded the threshold by $10
million.

     The Committee also noted that the acquisition of producing reserves was a
Company goal set at the beginning of 1998 that was not achieved.  The Committee
believes that given unstable market conditions during the year the executive
officers wisely refrained from participating in an unstable acquisition market
and instead positioned the Company to be able to take advantage of a more
attractive acquisition market expected in 1999.

      The Compensation Committee has reviewed the compensation of J. Darby Sere,
the Chairman of the Board and Chief Executive Officer, and William C. Rankin,
Senior Vice President and Chief Financial Officer, for the fiscal year ended
December 31, 1998 and has concluded that the compensation of each aforesaid
individual was reasonable in view of the Company's performance, their respective
contributions to that performance and general market conditions. Their
compensation was comprised of three elements: (1) base compensation; (2)
incentive bonus; and (3) stock options.

      Base Compensation.  The base salary decision takes into account the
employee's contributions to Company performance, internal equity among officers
and compensation set for comparable positions by the Company's competitors.  The
Compensation Committee analyzes proxy and annual report information to determine
base salaries paid by such peer group companies. The Committee determined that
Mr. Sere's salary was below the mean and median of the Company's peer group and
therefore, effective 

                                      -11-
<PAGE>
 
October 1, 1998, increased his salary by $24,000 to $252,000. The Committee also
took into account Mr. Sere's leadership role in several cost savings measures
including the reduction of the Company's administrative services fee with Torch
Energy Advisors Incorporated and the closing of an office of the Company in
Dallas, his development of an active acquisitions program as well as an
integrated team approach to exploration, exploitation and acquisition efforts,
his supervision of a stock buyback program, and his contributions to the growth
of the Company's capital budget and increased oil and gas production.

      Effective October 1, 1998, the Committee also increased Mr. Rankin's
salary by $9,600 to $183,600, taking into account Mr. Rankin's material role in
negotiating the reduction of the Company's administrative services fee with
Torch Energy Advisors Incorporated and restructuring of the services contract,
his role in evaluating the closing of an office of the Company in Dallas, his
role in evaluating the stock buyback program, his role in evaluating a cost-
saving interest rate swap, and his role in negotiating an amendment to the
Company's bank credit agreement.

     Bonus Compensation.  For his contributions during fiscal 1998, Mr. Sere was
granted a bonus of $100,800, representing approximately 40% of his base salary,
and Mr. William C. Rankin was granted a bonus of $45,900, representing
approximately 25% of his base salary.

      In awarding bonus compensation, the Committee took several factors into
account in addition to market conditions and the factors set forth above under
"Base Compensation." During 1998, through management's efforts the Company
successfully built an inventory of high-impact, technology-driven prospects for
drilling in 1999 and beyond.  Moreover, the Committee also noted that bonuses
for performance during 1997 were, based on the pool created by the Annual and
Long-Term Incentive Plan, underpaid by a significant amount.

      Stock-Based Compensation.  The Compensation Committee believes that stock
options serve as important long term incentives for executive officers of the
Company by encouraging continued employment and commitment to the performance of
the Company.  Moreover, the Compensation Committee believes that stock options
are an excellent means to align the interests of the Company's officers with
those of its stockholders.

      The number of options that the Compensation Committee grants to executive
officers is based on individual performance and level of responsibility. In
addition, the Compensation Committee strives to grant options at a level
sufficient to provide a strong incentive for executives to work for the long-
term success of the Company. The Compensation Committee considers the number of
options and terms thereof currently held by an executive officer in determining
individual grants, to ensure that the terms of the options, in light of
prevailing economic conditions, have not lost their incentive value.

      Taking into account the above factors, in 1998 the Committee granted
additional stock option awards to the Company's employees.  In particular, the
Committee awarded an option to Mr. Sere to purchase 54,000 shares of Common
Stock and an option to Mr. Rankin to purchase 24,000 shares of Common Stock.
See "Executive Compensation."  In 1999, the Committee granted an additional
30,000 stock options to Mr. Rankin in order to maintain an overall competitive
compensation package.

      The main elements of the Company's compensation policy of base salary,
bonus and stock options constitute an appropriate reward for the short and long-
term efforts of the Company's officers and officers of its principal
subsidiaries in order to support the future development of the Company and
growth in stockholder value.

                                 Dr. Jack Birks
                               Vincent H. Buckley
                                A. K. McLanahan

                                      -12-
<PAGE>
 
                       TRANSACTIONS WITH RELATED PERSONS

Relationship with Torch and Affiliates

      Administrative Services Agreement

      The Company has been party to the Administrative Services Agreement with
Torch since 1987.  Torch, headquartered in Houston, Texas, is primarily engaged
in the business of providing outsourcing services for clients in the energy
industry with respect to the acquisition and divestiture, exploration,
development, exploitation and operation of oil and gas properties, including
management advisory services, legal, financial and accounting services, and the
marketing of oil and gas.  In addition, Torch provides energy industry
investment management and advisory services for public companies and private
investors.  The Administrative Services Agreement is subject to termination by
the Company upon one year's prior notice.  The Administrative Services Agreement
has an initial term expiring on December 31, 1999 and may not be terminated by
Torch prior to such date.  The Company and Torch are currently renegotiating the
terms of the Administrative Services Agreement.  No new terms have been
definitively agreed upon.

      The Administrative Services Agreement requires Torch to administer certain
activities of the Company for a monthly fee.  These administrative services
include providing the Company with office space, equipment and supplies,
accounting, legal, financial, information technology and risk management
support, maintaining the books and records of the Company and preparing any
reports or other documents required by governmental authorities.  The Company
was also provided with geological and engineering services under the Agreement
until July 1998 when the Company brought such functions in house.  The Company
presently intends to continue to operate under the Administrative Services
Agreement or its replacement.

      The monthly fee payable to Torch under the Administrative Services
Agreement is equal to (i) one-twelfth of 2% of the book value of the Company's
assets, excluding cash and cash equivalents, plus (ii) 2% of operating cash
flows during such month less 20% of operator's overhead charged on Torch
operated properties.  The fees paid for the fiscal year ended December 31, 1998,
were $4 million.  The Company believes that the terms and fees under the
Administrative Services Agreement are comparable with those that could be
negotiated with a third party in an arm's length transaction and are fair to the
Company.

      Under the Administrative Services Agreement, the monthly fee for
administrative services does not apply to extraordinary investing and financing
services that Torch may agree to provide to the Company upon the Company's
request.  For such investing and financing services the Company pays Torch a fee
on an hourly basis for Torch employees providing such services, certain overhead
expenses with respect to such Torch employees and any related expenses.  The
Company did not pay any fees for these services during the fiscal year ended
December 31, 1998.

      The Company has agreed to indemnify Torch and its affiliates for
liabilities incurred by Torch or its affiliates for actions taken under the
Administrative Services Agreement, other than acts of fraud, willful misconduct
or gross negligence of Torch or its affiliates or any of their employees.

      The Compensation Committee of the Board of Directors, which is composed of
persons who are not employees of Torch or the Company, meets periodically to
review Torch's performance under the Administrative Services Agreement.  In
addition, a Special Committee of the Board of Directors, which is composed of
persons who are not affiliated with Torch, was formed to monitor negotiations
related to the Administrative Services Agreements.

                                      -13-
<PAGE>
 
      Other Relationships with Torch

      Torch markets a portion of the oil and natural gas production for certain
properties in which the Company owns an interest.  For the fiscal year ended
December 31, 1998, marketing fees paid by the Company to Torch amounted to
$1.143 million.

      Torch began operating the Snyder Gas Plant ("Gas Plant") in December 1993
pursuant to an operating agreement with the Company and other interest owners in
the Gas Plant.  The amount paid to Torch in connection with such operations
during the fiscal year ended December 31, 1998 was $72,000.

      Torch operates certain oil and gas interests owned by the Company.  The
Company is charged, on the same basis as other third parties, for all customary
expenses and cost reimbursements associated with these activities.  Torch's
overhead charges to the Company for these activities for the fiscal year ended
December 31, 1998 were $1.349 million.

      Costs of evaluating potential property acquisitions and due diligence
conducted in conjunction with acquisitions are incurred by Torch at the
Company's request.  The Company was charged $379,000 for such costs in the
fiscal year ended December 31, 1998.

      Ownership of Torch

      On September 30, 1996, Torch Acquisition Company ("TAC"), a company formed
by executive management of Torch, acquired all of the outstanding shares of
capital stock of Torch from United Investors Management Company ("United"), a
subsidiary of Torchmark Corporation.  J.P. Bryan, a director of the Company, is
the Senior Managing Director of TAC and owns 120,920 shares of common stock of
TAC, representing 23% of the shares of TAC on a fully diluted basis.

      Mining Ventures

      During fiscal year 1992, the Company acquired an average 24.4% interest in
three mining ventures (the "Mining Ventures") from an unaffiliated person for
$128,500.  At the time of such acquisition, Mr. Bryan, his brother, Shelby
Bryan, and Robert L. Gerry III, a director of Nuevo Energy Company (the
"Affiliated Group"), owned an average 21.5% interest in the Mining Ventures.
The Company's interest in the Mining Ventures increases as it pays costs of the
venture while the interest of the Affiliated Group decreases.  In 1998, the
Company invested $88,000, bringing the total investment to $476,000 as of
December 31, 1998.  The Company wrote down the value of the assets by $465,000
at December 31, 1998.

      Loan to Executive Officer

      On September 3, 1998, the Company agreed to establish a line of credit in
favor of J. Darby Sere in an amount up to $200,000.  Amounts outstanding under
the line of credit bear interest at a variable rate equivalent to a comparable
broker loan rate and are due and payable on September 30, 1999.  As of December
31, 1998, the outstanding balance under the line of credit was $150,000.  Mr.
Sere borrowed an additional $25,000 under the line of credit on each of January
25, 1999 and February 4, 1999.  As of March 31, 1999, the outstanding balance
under the line of credit was $200,000.  On February 9, 1999, the Company agreed
to loan Mr. Sere an additional $318,700.  The loan bears interest at a variable
rate equivalent to a comparable broker loan rate and is due and payable on May
9, 1999.  As of March 31, 1999, the outstanding balance under the loan was
$318,700.

                                      -14-
<PAGE>
 
                               PERFORMANCE GRAPH

      The following graph compares the yearly percentage change in the Company's
cumulative total stockholder return on its Common Stock (assuming reinvestment
of dividends at a date of payment into Common Stock of the Company) to the
cumulative total return on the NASDAQ Market Index ("Broad Market") and the
cumulative total return on the Dow Jones Secondary Oil Index ("Industry Index")
for the period of five and one-half years commencing June 30, 1993 and ending
December 31, 1998.

<TABLE>
<CAPTION>
                                         Bellwether                Industry Index               Broad Market
                                    --------------------        --------------------        --------------------
<S>                                 <C>                         <C>                         <C>
 
Fiscal Year Ending 6/93                      100                           100                       100
Fiscal Year Ending 6/94                   122.22                        101.31                    109.66
Fiscal Year Ending 6/95                   133.33                        107.27                    128.61
Fiscal Year Ending 6/96                   133.33                        128.13                    161.89
Fiscal Year Ending 6/97                   222.92                        152.08                    195.02
Transition Period Ending 12/97            244.44                        156.05                    213.05
Fiscal Year Ending 12/98                  109.72                        104.58                    300.49
</TABLE>

            SECTION 16(A) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE

      Section 16(a) of the Securities Exchange Act of 1934, as amended
("Exchange Act"), requires the Company's directors and executive officers, and
persons who own more than ten percent of a registered class of the Company's
equity securities, to file with the Commission and any exchange or other system
on which such securities are traded or quoted, initial reports of ownership and
reports of changes in ownership of Common Stock and other equity securities of
the Company.  Officers, directors and greater than ten percent stockholders are
required by the Commission's regulations to furnish the Company and any exchange
or other system on which such securities are traded or quoted with copies of all
Section 16(a) forms they filed with the Commission.

      To the Company's knowledge, based solely on a review of the copies of such
reports furnished to the Company and written representations that no other
reports were required, the Company believes that all reporting obligations of
the Company's officers, directors and greater than ten percent shareholders
under Section 16(a) were satisfied during the fiscal year ended December 31,
1998.

                STOCKHOLDERS' PROPOSALS FOR 2000 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 2000 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 Bellwether 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 2000 Annual Meeting of the Stockholders of the Company must be received
by the Secretary of the Company not less than 120 days in advance of April 28,
2000.  Such proposals must be in conformity with all applicable 

                                      -15-
<PAGE>
 
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 2000 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 14,
2000, unless the Company changes the date of its 2000 Annual Meeting of
Stockholders by more than 30 days from the date of the 1999 Annual Meeting of
Stockholders, 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 2000 Annual Meeting of
Stockholders.

      If the date of the 2000 Annual Meeting of Stockholders is advanced or
delayed by more than 30 calendar days from the date of the 1999 Annual Meeting
of Stockholders, 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.

                                 OTHER MATTERS

      The cost of soliciting proxies, including the cost of preparing and
mailing this Proxy Statement and the expenses incurred by brokerage houses
nominees and fiduciaries in forwarding proxy materials to beneficial owners,
will be borne by the Company.  In addition to solicitation by mail, certain
directors, officers and regular employees of the Company may solicit the return
of proxies by telephone, telecopy, fax telegram or personal interview.  Such
persons will receive no additional compensation for such services.

     The Board of Directors has no information that any matters other than those
referred to in this Proxy Statement will be brought before the Annual Meeting.
If, however, other matters should properly come before the meeting, the
accompanying proxy confers discretionary authority on the persons named therein
to vote thereon in accordance with the recommendations of the Board of
Directors.

                                    By Order of the Board of Directors

                                    /s/ ROBERT J. BENSH
                                    --------------------------------------
                                    Robert J. Bensh
                                    Secretary

April 28, 1999

     COPIES OF THE COMPANY'S ANNUAL REPORT AND THE COMPANY'S REPORT ON FORM 10-K
FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998, ARE AVAILABLE AT NO COST TO THE
STOCKHOLDERS OF THE COMPANY UPON WRITTEN REQUEST TO ROBERT J. BENSH, SECRETARY
OF THE COMPANY, AT 1331 LAMAR STREET, SUITE 1455, HOUSTON, TEXAS 77010-3039.

                                      -16-
<PAGE>
 
PROXY

                        BELLWETHER EXPLORATION COMPANY
               1331 LAMAR, SUITE 1465, HOUSTON, TEXAS 77010-3039

  PROXY SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS OF THE COMPANY FOR THE 
                        ANNUAL MEETING ON MAY 28, 1999

        The undersigned hereby constitutes and appoints J. Darby Sere and 
William C. Rankin and each of them, his true and lawful agents and proxies with 
full power of substitution in each, to represent and to vote, as designated on 
the reverse side, all of the shares of common stock of Bellwether Exploration 
Company held of record by the undersigned on April 13, 1999 at the Annual 
Meeting of Stockholders to be held at the Houston Center Club, 1100 Caroline 
Street, Houston, Texas on Friday, May 28, 1999, and at any adjournments thereof,
on all matters coming before said meeting.

        THIS PROXY, WHEN PROPERLY EXECUTED, WILL BE VOTED IN THE MANNER DIRECTED
HEREIN. IF NO DIRECTION IS MADE, THIS PROXY WILL BE VOTED FOR THE ELECTION OF 
DIRECTORS.

        THE BOARD OF DIRECTORS RECOMMENDS A VOTE FOR THE ELECTION OF DIRECTORS.

        YOU ARE ENCOURAGED TO SPECIFY YOUR CHOICES BY MARKING THE APPROPRIATE 
BOX (SEE REVERSE SIDE) BUT YOU NEED NOT MARK ANY BOXES IF YOU WISH TO VOTE IN 
ACCORDANCE WITH THE BOARD OF DIRECTORS' RECOMMENDATIONS. THE PROXIES CANNOT VOTE
YOUR SHARES UNLESS YOU SIGN AND RETURN THIS CARD.

                        (continued on the reverse side)

<PAGE>
 
                Please Detach and Mail in the Envelope Provided

A [X] Please mark your
      votes as in this
      example.


                                 FOR    WITHHELD
1. Election of Directors         [_]       [_]

To withhold authority to vote for any specific nominee(s), mark the "FOR"
box and write the name of each such nominee on the line provided below.

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

NOMINEES:   J. Darby Sere
            Dr. Jack Birks
            J.P. Bryan    
            Vincent H. Buckley
            Habib Kairouz
            A.K. McLanahan
            Townes G. Pressler

2. In their discretion, the Proxies are authorized to vote upon such other 
   business as may properly come before the meeting or any adjournments thereof.

Please check box if you plan to attend the annual meeting on May 28, 1999.  [_]

PLEASE MARK, SIGN, DATE AND RETURN THE PROXY CARD PROMPTLY IN THE STAMPED, 
PRE-ADDRESSED ENVELOPE ENCLOSED.


SIGNATURE(S)                                                    Date        
            --------------------------------------------------      ------------
NOTE: Please sign exactly as name appears hereon. Joint owners should each sign.
      When signing as attorney, executor, administrator, trustee or guardian,
      please indicate your full title as such.




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