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                                                                     EXHIBIT 4.1

                         SOUTHERN MINERAL CORPORATION

                    Series B Perpetual Warrant Certificate
          Representing Warrants to Purchase Shares of Common Stock,
                           Par Value $0.01 Per Share

     This Warrant Certificate certifies that, [_____________________] (including
its successors, the "HOLDER"), is the holder of [______] Series B Perpetual
Warrants ("WARRANTS"), each of which entitles such Holder to purchase, at any
time, one share (as adjusted) of common stock, par value $0.01 per share
("COMMON STOCK"), of Southern Mineral Corporation, a Nevada corporation (the
"COMPANY"), as such stock is constituted at the date of this warrant, at the
price of $4.21 per share (as adjusted, the "WARRANT PRICE"), but such number of
shares and the Warrant Price may be adjusted from time to time upon the
occurrence of certain events as provided in the Warrant Agreement (hereinafter
defined), by the surrender of this Warrant Certificate, with the subscription
form on the reverse side hereof duly executed, at the office of American Stock
Transfer & Trust Company, a New York corporation (the "WARRANT AGENT"), whose
address is 6201 Fifteenth Avenue, New York, New York, 11219, and the payment of,
in lawful money of the United States, the Warrant Price for the number of whole
shares of Common Stock as to which Warrants represented by this Warrant
Certificate are exercised, subject to the conditions set forth herein.

     Upon exercise of less than the full number of Warrants represented by this
Warrant Certificate, there shall be countersigned and issued to or upon the
order of the Holder a new Warrant Certificate in respect of the Warrants as to
which this Warrant Certificate shall not have been exercised.

     This Warrant Certificate may be exchanged either separately or in
combination with one or more other countersigned Warrant Certificates for one or
more new countersigned Warrant Certificates representing the same aggregate
number of Warrants represented by the Warrant Certificate or Warrant
Certificates exchanged.

     No fractional shares of Common Stock will be issued upon the exercise of
rights to purchase hereunder; rather, a cash payment in respect thereof will be
made by the Company in lieu of the issuance of a fractional share as provided in
the Warrant Agreement.

     No holder of this Warrant Certificate or of any Warrant shall be deemed to
be the holder of Common Stock or any other securities of the Company that may at
any time be issuable on the exercise hereof for any purpose, nor shall anything
contained in the Warrant Agreement or herein be construed to confer upon any
holder of this Warrant Certificate or of any Warrant, as such, any of the rights
of a stockholder of the Company or any right to vote for the election of
directors or upon any matter submitted to stockholders at any meeting thereof,
or to give or withhold consent to any corporate action (whether upon any
reorganization, issuance of securities, reclassification or conversion of Common
Stock, consolidation, merger, sale, lease, conveyance or otherwise), receive
notice of meetings or other action affecting stockholders (except for
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notices expressly provided for in the Warrant Agreement) or receive dividends or
subscription rights or otherwise.

     This Warrant Certificate is issued under and in accordance with the Series
B Perpetual Warrant Agreement dated as of [_________], 2000 (the "WARRANT
AGREEMENT"), between the Company and the Warrant Agent and is subject to the
terms and provisions contained in such Warrant Agreement, to all of which terms
and provisions the Holder consents by acceptance hereof.

     This Warrant Certificate and all rights hereunder are transferable by the
registered holder hereof, in whole or in part, on the register of the Company,
upon surrender of this Warrant Certificate for registration of transfer at the
office of the Warrant Agent maintained for such purpose, duly endorsed by, or
accompanied by a written instrument of transfer in form satisfactory to the
Company and the Warrant Agent duly executed by, the holder hereof or his
attorney duly authorized in writing, with signature guaranteed as specified in
the attached Form of Assignment. Upon any partial transfer, the Company will
issue and deliver to such holder a new Warrant Certificate or Warrant
Certificates with respect to any portion not so transferred. No service charge
shall be made for any registration of transfer or exchange of this Warrant
Certificate, but the Company may require payment of a sum sufficient to cover
any tax or other governmental charge payable in connection herewith.

     Each taker and holder of this Warrant Certificate, by taking or holding the
same, consents and agrees that this Warrant Certificate, when duly endorsed in
blank, shall be deemed negotiable and that when this Warrant Certificate shall
have been so endorsed, the holder hereof may be treated by the Company, the
Warrant Agent and all other persons and entities dealing with this Warrant
Certificate as the absolute owner hereof for any purpose and as the person
entitled to exercise the rights represented hereby, or to the transfer hereof on
the register of the Company maintained by the Warrant Agent, notwithstanding any
notice to the contrary, but until such transfer on such register, the Company
and the Warrant Agent may treat the registered holder hereof as the owner hereof
for all purposes.

     This Warrant Certificate and the Warrant Agreement are subject to amendment
as provided in the Warrant Agreement.

           [The remainder of this page is intentionally left blank.]
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     This Warrant Certificate shall not be valid for any purpose until it shall
have been countersigned by the Warrant Agent.

                                    SOUTHERN MINERAL CORPORATION


                                    By:
                                           ------------------------------
                                    Name:
                                           ------------------------------
                                    Title:
                                           ------------------------------

COUNTERSIGNED:


AMERICAN STOCK TRANSFER & TRUST COMPANY
as Warrant Agent

By:
       ------------------------------
Name:
       ------------------------------
Title:
       ------------------------------


Dated __________________
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                    [FORM OF REVERSE OF WARRANT CERTIFICATE]

                           EXERCISE SUBSCRIPTION FORM

           (To be executed only upon exercise of Warrant Certificate)


To:  Southern Mineral Corporation

     The undersigned irrevocably exercises ______________ Warrants represented
by this Warrant Certificate for the acquisition of _____________ shares of
common stock, par value $0.01 per share, of Southern Mineral Corporation on the
terms and conditions specified in the within Warrant Certificate and the Warrant
Agreement therein referred to, surrenders this Warrant Certificate and all
right, title and interest herein to Southern Mineral Corporation, and directs
that the shares of common stock deliverable upon the exercise of this Warrant
Certificate be registered or placed in the name and at the address specified
below and delivered thereto.

Dated: __________________
                              __________________________(1)
                              (Signature of Owner)

                              __________________________
                              (Street Address)

                              __________________________
                              (City)  (State)  (ZIP Code)

                              Signature Guaranteed by:


                              _____________________________________


-------------------------
(1) The signature must correspond with the name as written upon the face of the
within Warrant Certificate in every particular, without alteration or
enlargement or any change whatever, and must be guaranteed by an eligible
guarantor institution pursuant to SEC Rule 17Ad-15.
-------------------------
Shares of Common Stock to be issued to:

Please insert Social Security or identifying number:

Name:
Street Address:
City, State and ZIP Code:


Any Warrants represented by this Warrant Certificate which are exercisable but
unexercised to be issued to:

Please insert Social Security or identifying number:

Name:
Street Address:
City, State and ZIP Code:
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                              [FORM OF ASSIGNMENT]

     FOR VALUE RECEIVED, the undersigned registered holder of the within Warrant
Certificate hereby sells, assigns and transfers unto the assignee(s) named below
(including the undersigned with respect to any shares of common stock for which
the Warrants represented by the within Warrant Certificate are exercisable but
the right to exercise for which is not being assigned hereby) all of the right
of the undersigned under the within Warrant Certificate, with respect to the
number of Warrants as are set forth below:

                                   Social Security
                                     or other
                                    identifying
Name(s) of                          number of        Number of Warrants
Assignees        Address            Assignee(s)        being assigned
---------        -------            -----------      ------------------



and does hereby irrevocably constitute and appoint _______________ the
undersigned's attorney to make such transfer on the books of Southern Mineral
Corporation maintained for that purpose with full power of substitution in the
premises.

Dated:     ______________________

                              __________________________(1)
                              (Signature of Owner)


                              __________________________
                              (Street Address)


                              __________________________
                              (City)  (State)  (ZIP Code)


                              Signature Guaranteed by:


                              _____________________________________


-------------------------
(1) The signature must correspond with the name as written upon the face of the
within Warrant Certificate in every particular, without alteration or
enlargement or any change whatever, and must be guaranteed by an eligible
guarantor institution pursuant to SEC Rule 17Ad-15.