Document:

<PAGE>

                                                                   EXHIBIT 10.39

[Logo] Compass Bank                                       Compass Bank
                                                          P.O. Box 4444
                                                          Houston, TX 77210-4444

September 2, 1999

Mr. Steven H. Mikel
President & CEO
Southern Mineral Corporation
1201 Louisiana Street, Suite 3350
Houston, Texas 77002-5609

     RE:  Amended and Restated Credit Agreement dated June 19, 1998, by and
          between Southern Mineral Corporation, SMC Ecuador, Inc., SMC
          Production Co., BEC Energy, Inc., Amerac Energy Corporation, Compass
          Bank and First Union National Bank (as subsequently amended, restated,
          and/or supplemented, the "Credit Agreement")

Dear Steve:

Section 2.5 (a) of the Credit Agreement shall be amended to change the date of
September 1, 1999, to September 30, 1999.

The above date extension is contingent upon the payment of a fee ("Extension
Fee") to the Lenders in the amount of $50,000, to be shared pro rata by the
Lenders.

In connection with the proceeds from the sale of the Borrower's interest in the
Texan Gardens field, the Lenders agree to waive the requirements of Section 5.23
of the Credit Agreement, thereby allowing the Borrower to retain the remainder
of the proceeds ("Remaining Proceeds") from the sale of its interests in the
Texan Gardens field after payment of the following:

  (i)  Payment to the Lenders of the Restructure Fee as provided in Section 2.26
       of the Credit Agreement.  Section 2.26 of the Credit Agreement is hereby
       amended to provide that such Restructure Fee is payable upon the
       Borrower's sale of its interests in the Texan Gardens field.
  (ii) Payment shall be made to the Lenders of the Extension Fee as provided
       herein.

The allowance to retain the Remaining Proceeds is further contingent upon the
Borrower providing to the Agent original checks written on the Borrower's
account, payable to vendors and other parties, including amounts due associated
with the sale of the Texan Gardens field (along with stamped addressed
envelopes) which are to be paid out of the Remaining Proceeds in an amount
totaling no less than the Remaining Proceeds.  Such checks will be mailed by the
Agent upon deposit of the Remaining Proceeds into Borrower's account.
<PAGE>

Mr. Steven H. Mikel
September 2, 1999
Page 2

Except as expressly provided herein, the Credit Agreement and the other Loan
Documents shall remain in full force and effect in accordance with their
respective terms and this letter shall not be construed to:

   (i)   impair the validity, perfection or priority of any lien or security
         interest securing the Obligations;
   (ii)  waive or impair any rights, powers or remedies of the Agent and the
         Lenders under the Credit Agreement and the other Loan Documents; or
   (iii) grant any forbearance periods or extend the term of the Credit
         Agreement or the time for payment of any of the Obligations, except as
         expressly provided herein.

No Event of Default and no Default is waived or remedied by the execution of
this letter by the Lenders, and any such Default or Event of Default heretofore
arising and currently continuing shall continue after the execution and delivery
hereof.  Nothing contained in this letter, nor any past indulgence by the
Lenders, nor any prior waiver or consents or any waivers or consents which may
hereafter be granted nor any other action or inaction on behalf of the Lenders
(i) shall constitute or be deemed to constitute a waiver of any Defaults or
Events of Default which exist or may exist under the Credit Agreement or any
other Loan Document, or (ii) shall constitute or be deemed to constitute an
election of remedies by the Lenders or a waiver of any of the rights or remedies
of the Lenders provided in the Credit Agreement or the other Loan Documents or
otherwise afforded at law or in equity.

THIS LETTER, THE AGREEMENT AND THE OTHER WRITTEN LOAN DOCUMENTS REPRESENT,
COLLECTIVELY, THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE
CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.

Sincerely,

COMPASS BANK

By: /s/  Dorothy Marchand Wilson
   -------------------------------
         Dorothy Marchand Wilson
         Senior Vice President

FIRST UNION NATIONAL BANK

By: Illegible Signature
   -------------------------------

Its:Senior Vice President
    -------------------------------
<PAGE>

Mr. Steven H. Mikel
September 2, 1999
Page 3

ACKNOWLEDGED AND AGREED:

SOUTHERN MINERAL CORPORATION

/s/ Steven H. Mikel
----------------------------
Steven H. Mikel
President<PAGE>
                                                                   EXHIBIT 10.40

                           [COMPASS BANK LETTERHEAD]

September 30, 1999

Mr. Steven H. Mikel
President & CEO
Southern Mineral Corporation
1201 Louisiana Street, Suite 3350
Houston, Texas 77002-5609

     RE:  Amended and Restated Credit Agreement dated June 19, 1998, by and
          between Southern Mineral Corporation, SMC Ecuador, Inc., SMC
          Production Co., BEC Energy, Inc., Amerac Energy Corporation, Compass
          Bank and First Union National Bank (as subsequently amended, restated,
          and/or supplemented, the "Credit Agreement")

Dear Steve:

Section 2.5 (a) of the Credit Agreement shall be amended to change the date of
September 30, 1999 to October 8, 1999.

Except as expressly provided herein, the Credit Agreement and the other Loan
Documents shall remain in full force and effect in accordance with their
respective terms and this letter shall not be construed to:

      (i)   impair the validity, perfection or priority of any lien or security
            interest securing the Obligations;
      (ii)  waive or impair any rights, powers or remedies of the Agent and the
            Lenders under the Credit Agreement and the other Loan Documents; or
      (iii) grant any forbearance periods or extend the term of the Credit
            Agreement or the time for payment of any of the Obligations, except
            as expressly provided herein.

No Event of Default and no Default is waived or remedied by the execution of
this letter by the Lenders, and any such Default or Event of Default heretofore
arising and currently continuing shall continue after the execution and delivery
hereof.  Nothing contained in this letter, nor any past indulgence by the
Lenders, nor any prior waiver or consents or any waivers or consents which may
hereafter be granted nor any other action or inaction on behalf of the Lenders
(i) shall constitute or be deemed to constitute a waiver of any Defaults or
Events of Default which exist or may exist under the Credit Agreement or any
other Loan Document, or (ii) shall constitute or be deemed to constitute an
election of remedies by the Lenders or a waiver of any of the rights or remedies
of the Lenders provided in the Credit Agreement or the other Loan Documents or
otherwise afforded at law or in equity.
<PAGE>

Mr. Steven H. Mikel
September 30, 1999
Page 2

THIS LETTER, THE AGREEMENT AND THE OTHER WRITTEN LOAN DOCUMENTS
REPRESENT, COLLECTIVELY, THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE
CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.

Sincerely,

COMPASS BANK

By:/s/ Dorothy Marchand Wilson
   ---------------------------
       Dorothy Marchand Wilson
       Senior Vice President

FIRST UNION NATIONAL BANK

By:  __________________________

Its:  __________________________

ACKNOWLEDGED AND AGREED:

SOUTHERN MINERAL CORPORATION

/s/ Michael. E. Luttrell
------------------------
Michael E. Luttrell
Vice President & CFO<PAGE>

                                                                   EXHIBIT 10.41

COMPASS BANK                                              Compass Bank
                                                          P.O. Box 4444
                                                          Houston, TX 77210-4444

October 8, 1999

Mr. Steven H. Mikel
President & CEO
Southern Mineral Corporation
1201 Louisiana Street, Suite 3350
Houston, Texas 77002-5609

     RE:  Amended and Restated Credit Agreement dated June 19, 1998, by and
          between Southern Mineral Corporation, SMC Ecuador, Inc., SMC
          Production Co., BEC Energy, Inc., Amerac Energy Corporation, Compass
          Bank and First Union National Bank (as subsequently amended, restated,
          and/or supplemented, the "Credit Agreement")

Dear Steve:

Section 2.5 (a) of the Credit Agreement shall be amended to change the date of
October 8, 1999 to October 15, 1999.

In response to your letter dated as of today, the Lenders would like to point
out that the Company has been able to get to this point of improvement due, in
part, to the cooperation of the Lenders, which have acted in good faith by,
among other things, not declaring certain Events of Default and by extending the
maturity of Tranche A, as the Borrower and the Lenders have attempted to resolve
outstanding issues.  We remain interested in working  with the Borrower and the
Co-Borrowers toward improving their financial condition and satisfying their
Obligations under the Credit Agreement.  We will respond shortly to some of the
comments contained in your letter of October 8, 1999.

Except as expressly provided herein, the Credit Agreement and the other Loan
Documents shall remain in full force and effect in accordance with their
respective terms and this letter shall not be construed to:

   (i)   impair the validity, perfection or priority of any lien or security
         interest securing the Obligations;
   (ii)  waive or impair any rights, powers or remedies of the Agent and the
         Lenders under the Credit Agreement and the other Loan Documents; or
   (iii) grant any forbearance periods or extend the term of the Credit
         Agreement or the time for payment of any of the Obligations, except as
         expressly provided herein.

No Event of Default and no Default is waived or remedied by the execution of
this letter by the Lenders, and any such Default or Event of Default heretofore
arising and currently
<PAGE>

Mr. Steven H. Mikel
October 8, 1999
Page 2

continuing shall continue after the execution and delivery hereof. Nothing
contained in this letter, nor any past indulgence by the Lenders, nor any prior
waiver or consents or any waivers or consents which may hereafter be granted nor
any other action or inaction on behalf of the Lenders (i) shall constitute or be
deemed to constitute a waiver of any Defaults or Events of Default which exist
or may exist under the Credit Agreement or any other Loan Document, or (ii)
shall constitute or be deemed to constitute an election of remedies by the
Lenders or a waiver of any of the rights or remedies of the Lenders provided in
the Credit Agreement or the other Loan Documents or otherwise afforded at law or
in equity.

All capitalized terms not otherwise defined herein shall have the same meaning
as set forth in the Credit Agreement.

As additional consideration for the waiver granted herein by the Lenders, the
Borrower and Co-Borrowers hereby release the Agent and the Lenders from any and
all known or suspected claims, actions, demands, or causes of action of whatever
kind or character arising on or prior to the date hereof.  IT IS EXPRESSLY
AGREED THAT THE CLAIMS RELEASED BY THE BORROWER AND THE CO-BORROWERS HEREBY
INCLUDE THOSE ARISING FROM OR IN ANY MANNER ATTRIBUTABLE TO THE NEGLIGENCE
(SOLE, CONCURRENT, ORDINARY, OR OTHERWISE), OF THE AGENT AND THE LENDERS, THEIR
RESPECTIVE REPRESENTATIVES, AGENTS, OFFICERS, DIRECTORS, EMPLOYEES, SUCCESSORS
AND ASSIGNS.  Notwithstanding any provision of this modification or any other
Loan Document, this section shall remain in full force and effect and shall
survive the delivery and payment of the Notes, this modification and the other
Loan Documents and the making, extension, renewal, modification, amendment or
restatement of any thereof.

THIS LETTER, THE CREDIT AGREEMENT AND THE OTHER WRITTEN LOAN DOCUMENTS
REPRESENT, COLLECTIVELY, THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE
CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.

Sincerely,
COMPASS BANK

By: /s/  Dorothy Marchand Wilson
   -------------------------------
         Dorothy Marchand Wilson
         Senior Vice President

FIRST UNION NATIONAL BANK

By: /s/ Robert R. Wetteroff
   -------------------------------

Its: Robert R. Wetteroff
    ------------------------------
     Senior Vice President

<PAGE>

Mr. Steven H. Mikel
October 8, 1999
Page 3

ACKNOWLEDGED AND AGREED:

SOUTHERN MINERAL CORPORATION

/s/ Steven H. Mikel
-------------------------------
Steven H. Mikel
President

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