1
                                                                    EXHIBIT 4.10

                                    AGREEMENT

         THIS AGREEMENT ("Agreement") is made and entered into effective as of
the 18th day of May, 2001, by and among South Texas Drilling & Exploration,
Inc., a Texas corporation (the "Company") and WEDGE Energy Services, L.L.C., a
Delaware limited liability company ("WEDGE").


                                   WITNESSETH:

         WHEREAS, on March 30, 2001, WEDGE purchased from the Company a 4.86%
Convertible Subordinated Debenture, Series A (the "Debenture") for a purchase
price of $9,000,000.00 pursuant to that certain Debenture Purchase Agreement and
Debenture Agreement (collectively known as the "Debenture Agreements"); and

         WHEREAS, the Debenture is convertible, upon the Company obtaining
shareholder approval, into 2,400,000 shares of the $0.10 par value Common Stock
of the Company (the "Common Stock"); and

         WHEREAS, the Company desires to cancel the Debenture by paying a sum
equal to $9,000,000.00 plus accrued interest since March 30, 2001.

         NOW THEREFORE, in consideration of the mutual covenants herein
contained, the Company and WEDGE hereby acknowledge and agree as follows:

         1. WEDGE has received from the Company Nine Million Dollars
($9,000,000.00) plus Fifty Nine Thousand Five Hundred Thirty-Five Dollars
($59,535.00), such sum being the amount of accrued interest under the Debenture
since March 30, 2001 to the date hereof, such amounts in the aggregate
constituting full payment of all amounts owing under the Debenture.

         2. The Debenture is hereby cancelled, and all obligations, rights or
duties owed to or held by WEDGE or the Company under the Debenture or Debenture
Agreements are hereby terminated without additional obligation, including,
without limitation, the right of WEDGE to convert the Debenture into 2,400,000
shares of Common Stock.

         3. WEDGE shall have no further recourse against the Company under the
Debenture or Debenture Agreements whatsoever.


                            (SIGNATURE PAGE FOLLOWS)

                                      -1-


   2



         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to
become effective the day and date first above written.

                                   SOUTH TEXAS DRILLING & EXPLORATION, INC.


                                   By:  /s/   Wm. Stacy Locke
                                      -----------------------------------------
                                              Wm. Stacy Locke, President


                                   WEDGE ENERGY SERVICES, L.L.C.


                                   By:  /s/   R. E. Blohm, Jr.
                                      -----------------------------------------
                                              R. E. Blohm, Jr., Vice President



                                      -2-