<PAGE>
 
                                                            EXHIBIT 10(g)(3)(ii)


              EXTENSION AGREEMENT TO CONTINUE EMPLOYMENT AGREEMENT
                   BETWEEN KENNETH R. GOOD ("EXECUTIVE") AND
          POGO PRODUCING COMPANY, A DELAWARE CORPORATION ("COMPANY"),
                        DATED EFFECTIVE FEBRUARY 1, 1997


          WHEREAS, Executive and Company are parties to an "Employment
Agreement" bearing an original "Effective Date" of February 1, 1996; and

          WHEREAS, February 1, 1997, (even date herewith) is hereby deemed to be
the "Renewal Date" in that Employment Agreement; and

          WHEREAS, Executive and Company each wish to extend said Employment
Agreement for an additional one-year period so as to terminate (unless further
extended) two years thereafter, (to-wit January 31, 1999); and

          WHEREAS, Company desires to retain the services of Executive for the
benefit of Company and its shareholders, and desires to induce Executive to
remain in its employ for that extended time period; and

          WHEREAS, Executive has agreed to continue to serve as an employee of
Company for the period specified herein from and after the date of this
Extension Agreement; and

          WHEREAS, Company and Executive desire to enter into this Extension
Agreement in order to formally secure for Company the benefit of the experience
and abilities of Executive, and to set forth the agreements and understandings
of Company and Executive; and

          WHEREAS, Company has advised Executive that execution and performance
of this Extension Agreement by Company has been duly authorized and approved by
all requisite corporate action on the part of the Company.
<PAGE>
 
          NOW, THEREFORE, in consideration of the foregoing and the mutual
promises and agreements herein contained, and in consideration of the sum of $10
paid by Company to Executive, receipt whereof is hereby acknowledged by
Executive, Executive and Company do hereby agree as follows:

          1.   The Employment Agreement between Executive and Company bearing an
"Effective Date" of February 1, 1996 and a "Renewal Date" which is deemed herein
to be February 1, 1997,  is hereby extended for an additional one-year period
commencing February 1, 1997 and ending January 31, 1999, unless such employment
period is hereafter further extended for an additional period by both Executive
and Company.

          2.   All provisions of the Employment Agreement between Executive and
Company dated as of February 1, 1996, and as it is herein amended,  are
continued in full force and effect without change as if the Employment Agreement
had been initially effective as of February 1, 1997.


                                             POGO PRODUCING COMPANY


                                             By: /s/ John O. McCoy, Jr.
                                                 -----------------------
                                                 Vice President and Chief
                                                 Administrative Officer


ATTEST:

/s/  Joe Ann Kingdon
-------------------------------
Assistant Corporate Secretary

                                             EMPLOYEE:


                                                 /s/ Kenneth R. Good
                                                 -----------------------