<PAGE>

                                                                     EXHIBIT 2.3

                         UNITED STATES BANKRUPTCY COURT
                           SOUTHERN DISTRICT OF TEXAS
                               VICTORIA DIVISION

IN RE:                             (S)
                                   (S)
SOUTHERN MINERAL CORPORATION,      (S)   CASE NO. 99-60359-V2-11
SMC PRODUCTION COMPANY,            (S)   CASE NO. 99-60360-V2-11
AMERAC ENERGY CORPORATION,         (S)   CASE NO. 99-60361-V2-11
BEC ENERGY, INC.,                  (S)   CASE NO. 99-60362-V2-11
SMC ECUADOR, INC.,                 (S)   CASE NO. 99-60363-V2-11
                                   (S)
     Debtors.                      (S)   Jointly Administered Under
                                   (S)   CASE NO. 99-60359-V2-11

                        SECOND MODIFICATION TO DEBTORS'

                     SECOND AMENDED PLAN OF REORGANIZATION

                               FILED MAY 2, 2000


                              Dated June 29, 2000
<PAGE>

     The Debtors' Second Amended Plan of Reorganization Filed May 2, 2000, as
amended on June 19, 2000 by the Modification to Debtors' Second Amended Plan of
Reorganization Filed May 2, 2000  is hereby further amended by this Second
Modification (as amended, the "Plan") as follows:

Section 1.  Amendment to Article I.

     Article I.D. of the Plan is deleted in its entirety and replaced by the
following Article I.D.:

     The Plan provides for the full satisfaction of Allowed Claims of the
Creditor Classes defined below.  Unsecured Creditors, other than holders of
Debentures, will receive periodic cash payments in the full amount of their
Allowed Claims.  Holders of Debentures will receive a single cash payment and
New Common Stock in exchange for the Debentures.  The Bank Secured Claim will be
refinanced and paid from the proceeds of the Take-out Loan.  The holders of
shares of Southern Mineral Common Stock will retain ownership of those shares,
subject to a one-for-five reverse stock split and will receive the New Warrants.

Section 2.  Amendments to Article III.

    (a)   Article III.B.6. of the Plan is deleted in its entirety and replaced
          by the following Article III.B.6.:

               Class 6 - Holders of Common Stock

               The holders of Common Stock shall retain their existing shares of
               Southern Mineral, subject to a one-to-five reverse stock split.
               Current stock options and warrants shall be retained with no
               change in terms and conditions, except to effectuate the one-to-
               five reverse split and as provided in the Plan.

               The holders of Common Stock shall also receive a pro rata share
               of the New Warrants as further described in Article IV.D.4 of the
               Plan.

Section 3.  Amendments to Article IV.

    (a)   Article IV.B.2 of the Plan is deleted in its entirety and replaced by
          the following Article IV.B.2.:

               Amended Articles of Incorporation and Amended ByLaws

     The Amended Articles of Incorporation and Amended ByLaws of the Reorganized
Southern Mineral will include any and all amendments necessary to satisfy,
implement and give effect to the provisions of the Plan and the Bankruptcy Code
and shall include, among other things, a provision prohibiting the issuance of
non-voting equity securities.  The Amended Articles of Incorporation and Amended
ByLaws will be filed in a Plan Supplement.  Consistent with the Plan, the
Amended Articles of Incorporation shall also include, among other things, a
provision authorizing the issuance of the New Common Stock and increasing (prior
to giving

                                       1
<PAGE>

effect to the 1:5 reverse stock split contemplated by Article IV.D.3) the
authorized Common Stock to 75,000,000 authorized shares of Common Stock.

     If appropriate or required by applicable non-bankruptcy law the Amended
Articles of Incorporation and Amended ByLaws of Reorganized Southern Mineral
will include any and all amendments necessary to satisfy, implement and give
effect to the issuance of the New Warrants.

    (b)  Article IV.C. of the Plan is amended by adding the following new
         sentence immediately before the last sentence:

         The ability to distribute the Cash Payment provided for in Article
         III.B.4.a. is subject to the approval by Bank One Texas, N.A. of in
         inclusion of such amount in the funding of the Take-out Loan.

    (c)  Article IV.D. of the Plan is amended by adding the following new
         Article IV.D.4.:

         New Warrants

               i.  Amount

     New Warrants to purchase a sufficient number of shares of Common Stock such
that the Class 6 holders of Interests upon exercise thereof would hold a total
of 40% of the outstanding Common Stock on a fully diluted basis (including the
22% proportional interest resulting from the retention of such Interest holders'
existing shares as provided for in Article III.B. 6. of the Plan) as if such
warrants were exercised on the grant date thereof. The New Warrants will be
perpetual.  Any additional Common Stock or instrument convertible into or
allowing purchase of Common Stock issued after the Effective Date by Reorganized
Southern Mineral, would dilute, on an equal basis, the New Common Stock, the New
Warrants and the Common Stock being retained by the Class 6 Interest holders
pursuant to the Plan.

               ii.  Price

     The exercise price of the New Warrants will be $4.21 per share to be paid
in cash when exercised, subject to adjustment for certain customary anti-
dilution protections for stock splits, stock dividends and other
recapitalization events.

               iii.  Authorization

     As of the Consummation Date, the issuance by Reorganized Southern Mineral
of the New Warrants is hereby authorized without further act or action under
applicable law, regulation, order or rule.  A number of shares of Common Stock
equal to the number of shares of Common Stock issuable upon the exercise of the
New Warrants shall be, and hereby are, reserved for issuance upon the exercise
of the New Warrants.

                                       2
<PAGE>

               iv.  Issuance

     The New Warrants authorized pursuant to Article IV.D.4.c. of the Plan shall
be issued by Reorganized Southern Mineral pursuant to the Plan without further
act or action under applicable law, regulation, order or rule.

               v.  Bankruptcy Code Section 1145

     The issuance of the New Warrants and the Common Stock issuable upon the
exercise of the New Warrants pursuant to the Plan are hereby authorized in
accordance with Section 1145 of the Bankruptcy Code.

    (d)   Article IV.E.2. of the Plan is deleted in its entirety and replaced by
          the following Article IV.E.2.:

                Board of Directors

                     On the Effective Date, the term of the current Board of
                Southern Mineral will expire. The Board of Reorganized Southern
                Mineral will initially consist of the following individuals:

                     i.  Two Incumbent Directors; and

                     ii.  Five New Directors whose names will be announced
                     prior to the termination of the Confirmation Hearing.

     Pursuant to the Amended Articles of Incorporation and Amended Bylaws, as
appropriate:

    i.   the number of directors serving on the Board of Reorganized Southern
Mineral will be fixed at seven (7) until the first annual or special
shareholders' meeting following the first anniversary of the Effective Date.
After the first anniversary of the Effective Date, the number of directors may
be increased or decreased by the Board; and

    ii.  the term of the initial directors serving on the Board of Reorganized
Southern Mineral will be until the first regularly scheduled annual
shareholders' meeting following the first anniversary of the Effective Date; and
thereafter, directors will be elected annually at the annual meeting of
shareholders.

Section 4.  Amendment to ARTICLE VI.

          Article VI. of the Plan is deleted in its entirety and replaced by the
          following Article VI.:

          SECURITIES TO BE ISSUED IN CONNECTION WITH THE PLAN

               On or before the Distribution Date, Reorganized Southern Mineral
          shall issue for distribution in accordance with the provisions of the
          Plan (i) all of the

                                       3
<PAGE>

          New Common Stock and (ii) all of the New Warrants as required for
          distribution pursuant to the provisions of the Plan. All securities to
          be issued will be deemed issued as of the Distribution Date regardless
          of the date on which they are actually distributed.

Section 5.  Amendments to Article VII

    (a)  Article VII.A. of the Plan is deleted in its entirety and
         replaced by the following Article VII.A.:

               DISTRIBUTIONS FOR CLAIMS ALLOWED AS OF THE CONSUMMATION DATE

                    Except as otherwise provided herein or as ordered by the
               Bankruptcy Court, distributions to be made on account of Claims
               that are Allowed Claims as of the Distribution Date shall be made
               on the Distribution Date, or as soon thereafter as practicable.
               The New Common Stock to be issued under the Plan shall be deemed
               issued as of the Distribution Date regardless of the date on
               which they are actually distributed so long as all shares of the
               New Common Stock are distributed to the appropriate indenture
               trustee, agent or servicer on the Distribution Date.
               Distributions on account of Claims that first become Allowed
               Claims after the Consummation Date shall be made pursuant to
               Articles III, VII, and IX of the Plan.

               DISTRIBUTIONS FOR INTERESTS ALLOWED AS OF THE CONSUMMATION DATE

                    Except as otherwise provided herein or as ordered by the
               Bankruptcy Court, distributions to be made on account of
               Interests that are Allowed Interests as of the Distribution Date
               shall be made on the Distribution Date, or as soon thereafter as
               practicable. The New Warrants to be issued to holders of Allowed
               Interests under the Plan shall be deemed issued as of the
               Distribution Date regardless of the date on which they are
               actually distributed so long as all such New Warrants are
               distributed to the Disbursing Agent or the appropriate, agent or
               servicer on the Distribution Date. Distributions on account of
               Interests that first become Allowed Interests after the
               Consummation Date shall be made pursuant to Articles III, VII,
               and IX of the Plan.

    (b)  Article VII.G. of the Plan is amended by changing the heading thereof
         to "Record Date for Distributions to Holders of Debentures and Common
         Stock," and by adding the following new paragraph after the existing
         paragraph:

                    At the close of business on the Distribution Record Date the
               transfer ledgers of the Common Stock shall be closed and there
               shall be no further changes in the record holders of the Common
               Stock. Reorganized Southern Mineral and the Disbursing Agent, if
               any, shall have no obligation to recognize any transfer of such
               Common Stock occurring after the Distribution Record Date and
               shall be entitled instead to recognize and deal for all purposes
               hereunder with only those record holders stated on the transfer
               ledgers as of the close of business on the Distribution Record
               Date.

                                       4
<PAGE>

   (c)  Article VII.I. of the Plan is deleted in its entirety and replaced by
        the following Article VII.I.:

          CALCULATION OF DISTRIBUTION AMOUNTS OF NEW COMMON STOCK AND NEW
          WARRANTS

               No fractional shares of New Common Stock or fractional New
          Warrants shall be issued or distributed under the Plan or by
          Reorganized Southern Mineral or any Disbursing Agent, indenture
          trustee, agent, or servicer.  Each Person entitled to receive New
          Common Stock or New Warrants will receive the total number of whole
          shares of New Common Stock or whole New Warrants to which such Person
          is entitled.  Whenever any distribution to a particular Person would
          otherwise call for distribution of a fraction of a share of New Common
          Stock or fractional New Warrant, the Allowed Debenture Claim or the
          Allowed Interest, as applicable, producing the de minimis distribution
          shall be cancelled and discharged, and shall be of no further force
          and effect.  Upon the allocation of all the whole shares authorized
          under the Plan, all remaining shares of New Common Stock or New
          Warrants on account of fractional portions shall be cancelled, and no
          consideration shall be paid in respect of such cancelled fractional
          shares.

Section 6.  Amendments to Article XIII

   (a)  Article XIII.L. of the Plan is deleted in its entirety and replaced by
        the following Article XIII.L.:

               Any and all exhibits, lists or schedules not filed with the Plan
          shall be contained in a Plan Supplement and filed with the Clerk of
          the Bankruptcy Court prior to the Confirmation Date.  Notice of the
          filing of the Plan Supplement and the Plan Supplement will be sent to
          counsel for the Creditors' Committee by overnight mail or hand
          delivery.  Holders of Claims and Interests may obtain a copy of the
          Plan Supplement upon written request to Southern Mineral.

Section 7.  Amendments to Appendix I-A.

   (a)  The definition of "Cash Payment" in Appendix I-A to the Plan is deleted
        in its entirety and replaced by the following definition of such term:

          Cash Payment- shall mean Five Million United States Dollars ($US
          5,000,000.00).

   (b)  The definition of "New Director" in Appendix I-A to the Plan is deleted
        in its entirety and replaced by the following definition of such term:

          New Director -shall mean each of the following: (a) Gary L. Chitty and
               David E. Fite, provided, however, if either or both choose not to
               serve then the Creditors' Committee shall select one or two, as
               the case may be,

                                       5
<PAGE>

               Debenture holder(s) (other than from the Bondholder Group)
               willing to serve and reasonably acceptable to the Debtors prior
               to June 30, 2000 as a replacement(s), provided further, however,
               if such a replacement(s) is not timely made the Debtors shall
               select the replacement(s) from the Debenture holder group; and
               (b) three (3) individuals selected by the Bondholder Group,
               willing to serve and reasonably acceptable to the Debtors, prior
               to June 30, 2000, provided, however, that if such individuals are
               not either appointed or approved prior to June 30, then the board
               positions vacant at such time will not be filled and such vacant
               positions shall be filled by vote of the record holders of Common
               Stock in Reorganized Southern Mineral at a special shareholders'
               meeting to be called no later than ninety (90) days following the
               Distribution Date.

   (c)  The following definitions are inserted in alphabetical order in
        Appendix I-A to the Plan:

          Bondholder Group - shall mean Co-Mac Partners, L.P., Co-Mac Endowment,
               L.P., Co-Mac Int'l, N.V., Co-Mac Opportunities L.P., Jude Z.
               Nash, IRA, Robert Nash, IRA, Robert Nash and Paul Miller,
               including their respective insiders as that term is defined in
               section 101(31) of the Bankruptcy Code.

          New Warrants - shall have the meaning set forth in Article IV.D.4. of
               the Plan


EXCEPT AS EXPRESSLY MODIFIED BY THIS SECOND MODIFICATION, THE TERMS AND
CONDITIONS OF DEBTORS' SECOND AMENDED PLAN OF REORGANIZATION FILED MAY 2, 2000,
AS AMENDED ON JUNE 19, 2000 BY THE MODIFICATION TO DEBTORS' SECOND AMENDED PLAN
OF REORGANIZATION FILED MAY 2, 2000 REMAIN IN FULL FORCE AND EFFECT.




                   REMAINDER OF PAGE INTENTIONALLY LEFT BLANK

                                       6
<PAGE>

Dated:  June 29, 2000
        Houston, Texas

                              SOUTHERN MINERAL CORPORATION

                              /s/ Steven H.Mikel
                              -----------------------------------
                              Steven H. Mikel
                              President, Chief Executive Officer and Secretary


                              SMC PRODUCTION COMPANY

                              /s/ Steven H.Mikel
                              -----------------------------------
                              Steven H. Mikel
                              President, Chief Executive Officer and Secretary


                              AMERAC ENERGY CORPORATION

                              /s/ Steven H.Mikel
                              -----------------------------------
                              Steven H. Mikel
                              President, Chief Executive Officer and Secretary


                              BEC ENERGY, INC.

                              /s/ Steven H.Mikel
                              -----------------------------------
                              Steven H. Mikel
                              President, Chief Executive Officer and Secretary


                              SMC ECUADOR, INC.

                              /s/ Steven H.Mikel
                              -----------------------------------
                              Steven H. Mikel
                              President, Chief Executive Officer and Secretary

Akin, Gump, Strauss, Hauer & Feld, L.L.P.
Attorneys for Debtors


By: /s/ H. Rey Stroube, III
   -------------------------
      H. Rey Stroube, III

                                       7