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                               State of Delaware

                       Office of the Secretary of State


     I, EDWARD J. FREEL, SECRETARY OF STATE OF THE STATE OF DELAWARE, DO HEREBY 

CERTIFY THE ATTACHED IS A TRUE AND CORRECT COPY OF THE CERTIFICATE OF 

DESIGNATION OF "BELLWETHER EXPLORATION COMPANY", FILED IN THIS OFFICE ON THE 

NINETEENTH DAY OF SEPTEMBER, A.D. 1997, AT 3:15 O'CLOCK P.M.

     A CERTIFIED COPY OF THIS CERTIFICATE HAS BEEN FORWARDED TO THE NEW CASTLE 

COUNTY RECORDER OF DEEDS FOR RECORDING.





                                             /s/ EDWARD J. FREEL
                                            ____________________________________
                                            Edward J. Freel, Secretary of State

                                            AUTHENTICATION:   86661211

                                                      DATE:   09-22-97
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              CERTIFICATE OF DESIGNATION, PREFERENCES AND RIGHTS

                          OF SERIES A PREFERRED STOCK

                                      OF

                        BELLWETHER EXPLORATION COMPANY

                    PURSUANT TO SECTION 151 OF THE GENERAL
                   CORPORATION LAW OF THE STATE OF DELAWARE


     I, J. Darby Sere, Chairman and Chief Executive Officer of Bellwether 
Exploration Company, a corporation organized and existing under the General 
Corporation Law of the State of Delaware (the "Corporation"), in accordance 
with the provisions of Section 103 thereof, DO HEREBY CERTIFY:

     That pursuant to the authority conferred upon the Board of Directors by the
Certificate of Incorporation of the Corporation, the Board of Directors on 
September 12, 1997, adopted the following resolution creating a series of 
300,000 shares of Preferred Stock designated as Series A Preferred Stock.

     RESOLVED, that pursuant to the authority vested in the Board of Directors 
of this Corporation in accordance with the provisions of its Certificate of 
Incorporation, a series of Preferred Stock of the Corporation is hereby created,
and that the designation and amount thereof and the voting powers, preferences 
and relative, participating, optional and other special rights of the shares of 
such series, and the qualifications, limitations or restrictions thereof are as 
follows:

     SECTION 1.  DESIGNATION AND AMOUNT.  There shall be a series of Preferred 
Stock of the Corporation which shall be designated as "Series A Preferred 
Stock", par value $1.00 per share, and the number of shares constituting such
series shall be 300,000. Such number of shares may be increased or decreased by
resolution of the Board of Directors; provided, that no decrease shall reduce
the number of shares of Series A Preferred Stock to a number less than that of
the shares then outstanding plus the number of shares issuable upon exercise of
outstanding rights, options or warrants or upon conversion of outstanding
securities issued by the Corporation.

     SECTION 2.  DIVIDENDS AND DISTRIBUTIONS.  (A) Subject to the prior and 
superior rights of the holders of any shares of any series of Preferred Stock 
ranking prior and superior to the Series A Preferred Stock with respect to 
dividends, the holders of shares of Series A Preferred Stock in preference to 
the holders of shares of Common Stock, par value $.01 per share (the "Common 
Stock"), of the Corporation and any other junior stock, shall be entitled to 
receive, when, as and if declared by the Board of Directors out of funds legally
available for the purpose, quarterly dividends payable in cash on the first day 
of January, April, July, and October in each year (each such date being referred
to herein as a "Quarterly Dividend Payment Date"), commencing on the first 
Quarterly

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Dividend Payment Date after the first issuance of a share or fraction of a share
of Series A Preferred Stock in an amount per share (rounded to the nearest cent)
equal to the greater of (a) $.25 (twenty-five cents), or (b) subject to the 
provision for adjustment hereinafter set forth, 100 times the aggregate per 
share amount of all cash and non-cash (payable in kind) dividends or other 
distributions other than a dividend payable in shares of Common Stock or a 
subdivision of the outstanding shares of Common Stock or a subdivision of the 
outstanding shares of Common Stock (by reclassification or otherwise), declared 
on the Common Stock, since the immediately preceding Quarterly Dividend Payment 
Date, or, with respect to the first Quarterly Dividend Payment Date, since the 
first issuance of any share of fraction of a share of Series A Preferred Stock.
In the event the Corporation shall at any time after September 26, 1997 (the 
"Record Date") (i) declare any dividend on Common Stock payable in shares of 
Common Stock, (ii) subdivide the outstanding Common Stock, or (iii) combine the 
outstanding Common Stock into a smaller number of shares, then in each such case
the amount to which holders of shares of Series A Preferred Stock were entitled 
immediately prior to such event under clause (b) of the preceding sentence shall
be adjusted by multiplying such amount by a fraction the numerator of which is 
the number of shares of Common Stock outstanding immediately after such event 
and the denominator of which is the number of shares of Common Stock that were 
outstanding immediately prior to such event.

     (B) The Corporation shall declare a dividend or distribution on the Series 
A Preferred Stock as provided in paragraph (A) above immediately after it 
declares a dividend or distribution on the Common Stock (other than a dividend 
payable in shares of Common Stock); provided that, in the event no dividend or 
distribution shall have been declared on the Common Stock during the period 
between any Quarterly Dividend Payment Date and the next subsequent Quarterly 
Dividend Payment Date, a dividend of $.25 (twenty-five cents) per share on the 
Series A Preferred Stock shall nevertheless be payable on such subsequent 
Quarterly Dividend Payment Date.

     (C) Dividends shall begin to accrue and be cumulative on outstanding shares
of Series A Preferred Stock from the Quarterly Dividend Payment Date next 
preceding the date of issue of such shares of Series A Preferred Stock unless 
the date of issue of such shares is prior to the record date for the first 
Quarterly Dividend Payment Date, in which case dividends on such shares shall 
begin to accrue from the date of issue of such shares, or unless the date of 
issue is a Quarterly Dividend Payment Date or is a date after the record date 
for the determination of holders of shares of Series A Preferred Stock entitled 
to receive a quarterly dividend and before such Quarterly Dividend Payment Date,
in either of which events such dividends shall begin to accrue and be cumulative
from such Quarterly Dividend Payment Date.  Accrued but unpaid dividends shall 
not bear interest.  Dividends paid on the shares of Series A Preferred Stock in 
an amount less than the total amount of such dividends at the time accrued and 
payable on such shares shall be allocated pro rata on a share-by-share basis 
among all such shares at the time outstanding.  The Board of Directors may fix a
record date for the determination of holders of shares of Series A Preferred 
Stock entitled to receive payment of a dividend or distribution declared 
thereon, which record date shall be no more than 60 days prior to the date fixed
for the payment thereof.


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     SECTION 3.  VOTING RIGHTS.  The holders of shares of Series A Preferred 
Stock shall have the following voting rights:

     (A) Subject to the provision for adjustment hereinafter set forth, each 
share of Series A Preferred Stock shall entitle the holder thereof to 100 votes 
on all matters submitted to a vote of the stockholders of the Corporation.  In 
the event the Corporation shall at any time after the Rights Declaration Date 
(i) declare any dividend on Common Stock payable in shares of Common Stock, (ii)
subdivide the outstanding Common Stock, or (iii) combine the outstanding Common 
Stock into a smaller number of shares, then in each such case the number of
votes per share to which holders of shares of Series A Preferred Stock were
entitled immediately prior to such event shall be adjusted by multiplying such
number by a fraction the numerator of which is the number of shares of Common
Stock outstanding immediately after such event and the denominator of which is
the number of shares of Common Stock that were outstanding immediately prior to
such event.

     (B) Except as otherwise provided herein or by law, the holders of shares of
Series A Preferred Stock and the holders of shares of Common Stock shall vote
together as one class on all matters submitted to a vote of stockholders of the
Corporation.

     (C) (i) If at any time dividends on any Series A Preferred Stock shall be 
in arrears in an amount equal to six (6) quarterly dividends thereon, the 
occurrence of such contingency shall mark the beginning of a period (here called
a "default period") which shall extend until such time when all accrued and 
unpaid dividends for all previous quarterly dividend periods and for the current
quarterly dividend period on all shares of Series A Preferred Stock then 
outstanding shall have been declared and paid or set apart for payment.  During 
each default period, all holders of Preferred Stock (including holders of the 
Series A Preferred Stock) with dividends in arrears in an amount equal to six 
quarterly dividends thereon, voting as a class, irrespective of series, shall 
have the right to elect two Directors.

     (ii) During any default period, such voting right of the holders of Series 
A Preferred Stock may be exercised initially at a special meeting called 
pursuant to subparagraph (iii) of this Section 3(C) or at any annual meeting of 
stockholders, and thereafter at annual meetings of stockholders, provided that 
neither such voting right nor the right of the holders of any other series of 
Preferred Stock, if any, to increase, in certain cases, the authorized number of
Directors shall be exercised unless the holders of ten percent in number of 
shares of Preferred Stock outstanding shall be present in person or by proxy.  
The absence of a quorum of the holders of Common Stock shall not affect the 
exercise by the holders of Preferred Stock of such voting right.  At any meeting
at which the holders of Preferred Stock shall exercise such voting right 
initially during an existing default period, they shall have the right, voting 
as a class, to elect Directors to fill such vacancies, if any, in the Board of 
Directors as may then exist up to two Directors or, if such right is exercised 
at an annual meeting, to elect two Directors.  If the number which may be so 
elected at any special meeting does not amount to the required number, the 
holders of the Preferred Stock shall have the right to make such increase in the
number of Directors as shall be necessary to permit the election by them of the 
required number.  After the holders of the Preferred Stock shall have exercised


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their right to elect Directors in any default period and during the continuance 
of such period, the number of Directors shall not be increased or decreased 
except by vote of the holders of Preferred Stock as herein provided or pursuant 
to the rights of any equity securities ranking senior to or pari passu with the 
Series A Preferred Stock.

     (iii) Unless the holders of Preferred Stock shall, during an existing 
default period, have previously exercised their right to elect Directors, the 
Board of Directors may order, or any stockholder or stockholders owning in the 
aggregate not less than ten percent of the total number of shares of Preferred 
Stock outstanding, irrespective of series, may request, the calling of a special
meeting of the holders of Preferred Stock, which meeting shall thereupon be 
called by the President, a Vice President or the Secretary of the Corporation.  
Notice of such meeting and of any annual meeting at which holders of Preferred 
Stock are entitled to vote pursuant to this paragraph (C)(iii) shall be given to
each holder of record or Preferred Stock by mailing a copy of such notice to 
him at his last address as the same appears on the books of the Corporation.  
Such meeting shall be called for a time not earlier than 20 days and no later 
than 60 days after such order or request or, in default of the calling of such 
meeting within 60 days after such order or request, such meeting may be called
on similar notice by any stockholder or stockholders owning in the aggregate not
less than ten percent of the total number of shares of Preferred Stock
outstanding. Notwithstanding the provisions of this paragraph (C)(iii), no such
special meeting shall be called during the period within 60 days immediately
preceding the date fixed for the next annual meeting of the stockholders.

     (iv)  In any default period, the holders of Common Stock, and other classes
of stock of the Corporation if applicable, shall continue to be entitled to 
elect the whole number of Directors until the holders of Preferred Stock shall
have exercised their right to elect two Directors voting as a class, after the
exercise of which right (x) the Directors so elected by the holders of Preferred
Stock shall continue in office until their successors shall have been elected by
such holders or until the expiration of the default period, and (y) any vacancy
in the Board of Directors may (except as provided in paragraph (C)(ii) of this
Section 3) be filled by vote of a majority of the remaining Directors
theretofore elected by the holders of the class of stock which elected the
Directors elected by the holders of a particular class of stock shall include
Directors elected by such Directors to fill vacancies as provided in clause (y)
of the foregoing sentence.

     (v)   Immediately upon the expiration of a default period, (x) the right of
the holders of Preferred Stock as a class to elect Directors shall cease, (y) 
the term of any Directors elected by the holders of Preferred Stock as a class 
shall terminate, and (z) the number of Directors shall be such number as may be 
provided for in the Certificate of Incorporation or By-Laws irrespective of any 
increase made pursuant to the provisions of paragraph (C)(ii) of this Section 3 
(such number being subject, however, to change thereafter in any manner provided
by law or in the Certificate of Incorporation or By-Laws).  Any vacancies in the
Board of Directors effected by the provisions of clauses (y) and (z) in the 
preceding sentence may be filled by a majority of the remaining Directors.


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     (D) Except as set forth herein, holders of Series A Preferred Stock shall 
have no special voting rights and their consent shall not be required (except to
the extent they are entitled to vote with holders of Common Stock as set forth 
herein) for taking any corporate action.

     SECTION 4.  CERTAIN RESTRICTIONS.  (A) Whenever quarterly dividends or 
other dividends or distributions payable on the Series A Preferred Stock as 
provided in Section 2 are in arrears, thereafter and until all accrued and
unpaid dividends and distributions, whether or not declared, on shares of Series
A Preferred Stock outstanding shall have been paid in full, the Corporation
shall not:

          (i)   Declare or pay dividends on, make any other distributions on, or
     redeem or purchase or otherwise acquire for consideration any shares of
     stock ranking junior (either as to dividends or upon liquidation,
     dissolution or winding up) to the Series A Preferred Stock;

          (ii)  Declare or pay dividends on or make any other distributions on 
     any shares of stock ranking on a parity (either as to dividends or upon
     liquidation, dissolution or winding up) with the Series A Preferred Stock
     except dividends paid ratably on the Series A Preferred Stock and all such
     parity stock on which dividends are payable or in arrears in proportion to
     the total amounts to which the holders of all such shares are then
     entitled;

          (iii) Redeem or purchase or otherwise acquire for consideration shares
     of any stock ranking on a parity (either as to dividends or upon
     liquidation, dissolution or winding up) with the Series A Preferred Stock
     provided that the Corporation may at any time redeem, purchase or otherwise
     acquire shares of any such parity stock in exchange for shares of any stock
     of the Corporation ranking junior (either as to dividends or upon
     dissolution, liquidation or winding up) to the Series A Preferred Stock; or

          (iv)  Purchase or otherwise acquire for consideration any shares of 
     Series A Preferred Stock or any shares of stock ranking on a parity with
     the Series A Preferred Stock except in accordance with a purchase offer
     made in writing or by publication (as determined by the Board of Directors)
     to all holders of such shares upon such terms as the Board of Directors,
     after consideration of the respective annual dividend rates and other
     relative rights and preferences of the respective series and classes, shall
     determine in good faith will result in fair and equitable treatment among
     the respective series or classes.

     (B) The Corporation shall not permit any subsidiary of the Corporation to 
purchase or otherwise acquire for consideration any shares of stock of the 
Corporation unless the Corporation could, under paragraph (A) of this Section 4,
purchase or otherwise acquire such shares at such time and in such manner.

     SECTION 5.  REACQUIRED SHARES.  Any shares of Series A Preferred Stock 
purchased or otherwise acquired by the Corporation in any manner whatsoever
shall be retired and cancelled promptly after the acquisition thereof. All such
shares shall upon


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their cancellation become authorized but unissued shares of Preferred Stock and 
may be reissued as part of a new series of Preferred Stock to be created by 
resolution or resolutions of the Board of Directors, subject to the conditions 
and restrictions on issuance set forth herein.

     SECTION 6.  LIQUIDATION, DISSOLUTION OR WINDING UP.  (A) Upon any 
liquidation (voluntary or otherwise), dissolution or winding up of the 
Corporation, no distribution shall be made to the holders of shares of stock 
ranking junior (either as to the dividends or upon liquidation, dissolution or 
winding up) to the Series A Preferred Stock unless, prior thereto, the holders 
of shares of Series A Preferred Stock shall have received per share, the greater
of $.25 (twenty-five cents) or 100 times the payment made per share of Common 
Stock, plus an amount equal to accrued and unpaid dividends and distributions 
thereon, whether or not declared, to the date of such payment (the "Series A 
Liquidation Preference").  Following the payment of the full amount of the 
Series A Liquidation Preference, no additional distributions shall be made to 
the holders of shares of Series A Preferred Stock unless, prior thereto, the 
holders of shares of Common Stock shall have received an amount per share (the 
"Common Adjustment") equal to the quotient obtained by dividing (i) the Series A
Liquidation Preference by (ii) 100 (as appropriately adjusted as set forth in 
subparagraph C below to reflect such events as stock splits, stock dividends and
recapitalizations with respect to the Common Stock) (such number in clause (ii),
the "Adjustment Number").  Following the payment of the full amount of the 
Series A Liquidation Preference and the Common Adjustment in respect of all 
outstanding shares of Series A Preferred Stock and Common Stock, respectively, 
holders of Series A Preferred Stock and holders of shares of Common Stock shall 
receive their ratable and proportionate share of the remaining assets to be 
distributed in the ratio of the Adjustment Number to 1 with respect to such 
Preferred Stock and Common Stock, on a per share basis, respectively.

     (B) In the event there are not sufficient assets available to permit 
payment in full of the Series A Liquidation Preference and the liquidation 
preferences of all other series of Preferred Stock, if any, which rank on a 
parity with the Series A Preferred Stock, then such remaining assets shall be 
distributed ratably to the holders of such parity shares in proportion to their 
respective liquidation preferences.  In the event there are not sufficient 
assets available to permit payment in full of the Common Adjustment, then such 
remaining assets shall be distributed ratably to the holders of Common Stock.

     (C) In the event the Corporation shall at any time after the Record Date 
(i) declare any dividend on Common Stock payable in shares of Common Stock, (ii)
subdivide the outstanding Common Stock, or (iii) combine the outstanding Common 
Stock into a smaller number of shares, then in each such case the Adjustment 
Number in effect immediately prior to such event shall be adjusted by 
multiplying such Adjustment Number by a fraction the numerator of which is the 
number of shares of Common Stock outstanding immediately after such event and 
the denominator of which is the number of shares of Common Stock that were 
outstanding immediately prior to such event.

     SECTION 7.  CONSOLIDATION, MERGER, ETC.  In case the Corporation shall 
enter into any consolidation, merger, combination or other transaction in which 
the shares of Common Stock are exchanged for or changed into other stock or 
securities, cash and/or


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any other property, then in any such case the shares of Series A Preferred Stock
shall at the same time be similarly exchanged or changed in an amount per share 
(subject to the provision for adjustment hereinafter set forth) equal to 100 
times the aggregate amount of stock, securities, cash and/or any other property 
(payable in kind), as the case may be, into which or for which each share of 
Common Stock is changed or exchanged.  In the event the Corporation shall at any
time after the Rights Declaration Date (i) declare any dividend on Common Stock 
payable in shares of Common Stock, (ii) subdivide the outstanding Common Stock, 
or (iii) combine the outstanding Common Stock into a smaller number of shares, 
then in each such case the amount set forth in the preceding sentence with 
respect to the exchange or change of shares of Series A Preferred Stock shall be
adjusted by multiplying such amount by a fraction the numerator of which is the 
number of shares of Common Stock outstanding immediately after such event and 
the denominator of which is the number of shares of Common Stock that are 
outstanding immediately prior to such event.

     SECTION 8.  REDEMPTION.  The shares of Series A Preferred Stock shall not 
be redeemable.

     SECTION 9.  RANKING.  The Series A Preferred Stock shall rank junior to all
other series of the Corporation's Preferred Stock as to the payment of dividends
and the distribution of assets, unless the terms of any such series shall
provide otherwise.

     SECTION 10.  FRACTIONAL SHARES.  Series A Preferred Stock may be issued in 
fractions of a share which shall entitle the holder, in proportion to such 
holder's fractional shares, to exercise voting rights, receive dividends, 
participate in distributions and to have the benefit of all other rights of 
holders of Series A Preferred Stock.


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     IN WITNESS WHEREOF,  I have executed and subscribed this Certificate and do
affirm the foregoing as true under the penalties of perjury this 17th day of 
September, 1997.


                                          /s/ J. DARBY SERE
                                     By: _____________________________
                                     Name:  J. Darby Sere
                                     Title: Chairman and Chief Executive Officer


Attest:



/s/ ROLAND E. SLEDGE
___________________________
Roland E. Sledge, Secretary


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