<PAGE>   1
                                                                   EXHIBIT 10(e)


                   EXECUTIVE RETIREMENT SUPPLEMENT AGREEMENT

                 THIS EXECUTIVE RETIREMENT SUPPLEMENT AGREEMENT made effective
as of _________________________ between Energen Corporation, a corporation (the
"Company"), and ___________________________ (the "Executive").

                                R E C I T A L S

                 The Executive has been employed by the Company and/or one or
more of its subsidiaries for a number of years, and as an employee has provided
capable executive leadership and management so as to enable the Company to
operate efficiently and effectively.  The Company and the Executive desire to
enter into this Agreement to provide for payment to the Executive and the
Executive's eligible spouse certain deferred compensation in the form of a
retirement supplement under certain circumstances.

                 NOW, THEREFORE, in consideration of the mutual promises of the
parties and the parties agree as follows:

                            ARTICLE 1 -- DEFINITIONS

         1.1     Agreement:  This document, including any attached schedules,
and any amendments to the same.

         1.2     Birthday:  An anniversary of the Executive's birth regardless
of whether the Executive survives to such anniversary.

         1.3     Cause:  Termination of employment by the Employer for "Cause"
shall mean TERMINATION based on any of the following:

                 (a)      The willful and continued failure by the Executive to
substantially perform such Executive's duties with the Employer (other than any
such failure resulting from such Executive's incapacity due to physical or
mental illness) after a written demand for substantial performance is delivered
to the Executive specifically identifying the manner in which such Executive
has not substantially performed such Executive's duties;

                 (b)      The engaging by the Executive in willful misconduct
which is demonstrably injurious to the Employer monetarily or otherwise; or

                 (c)      The conviction of the Executive of a felony.

         1.4     Code:  The Internal Revenue Code of 1986, as the same may
from time to time be amended.





                                       1
<PAGE>   2
         1.5     Committee:  The Officers Review Committee of the Board of
Directors of the Company or any person or persons appointed by the Board of
Directors to administer the Agreement.

         1.6     Compensation:  The sum of A plus B.  For purposes of this
definition, A shall equal the average aggregate monthly basic pay from all
Employers for the 36 consecutive calendar months during which the Executive had
the highest average monthly basic pay out of the 60 calendar months immediately
preceding the Severance Date.  For purposes of this definition, B shall equal C
divided by 12, where C equals the average of the Executive's three highest
annual cash incentive awards under the Energen Annual Incentive Compensation
Plan (or successor annual cash incentive plan) for the five Company fiscal
years immediately preceding the earlier of (i) the fiscal year during which the
Severance Date occurs or (ii) the fiscal year during which the Executive's 61st
birthday occurs.

         1.7     Disability:  Total and permanent disability which entitles the
Executive to a disability benefit under the disability program sponsored and/or
maintained by the Company or the Executive's Employer.

         1.8     Eligibility Date:  The earliest date on which the Executive
could be entitled to receive the Executive's "primary insurance amount" or any
portion thereof under the federal Social Security Act as amended and in effect
on the Severance Date assuming that the Executive survives to such date.

         1.9     Employer:  The Company and any and all subsidiaries of the
Company and their respective successors and assigns.

         1.10    Lump Sum Election: An election made by the Executive pursuant
to Section 2.5 to receive a lump sum payment in lieu of the Supplemental
Retirement Benefit.

         1.11    Normal Retirement Date:  The first day of the month on or next
following the Executive's 60th Birthday; provided, however, if the Executive's
employment with an Employer continues beyond such date, the first day of the
month on or next following the date on which the Executive actually Retires
shall be  Normal Retirement Date.

         1.12    Present Value:  The present value of a benefit or benefits
determined using the discount rate used to determine the present value of
payments under Section 280G of the Code that is in effect at the date payment
is to be made and the mortality assumptions utilized to determine actuarial
equivalent benefits under the Retirement Plan at that date.

         1.13    Retire or Retirement:  Termination of employment (for whatever
reason including death) from all Employers after attaining age 60.

         1.14    Retirement Plan:  The "Energen Corporation Retirement Income
Plan," as the same may be amended and in effect from time to time hereafter.





                                       2
<PAGE>   3

         1.15    Retirement Plan Benefit:  The monthly amount of retirement
benefit payable to the Executive from the Retirement Plan in the normal form,
with no election of an optional form of payment, calculated under the terms of
the Retirement Plan as in effect on the Severance Date and with the following
assumptions: (i) the Executive will accrue no Years of Service or partial Years
of Service under the Retirement Plan after the Severance Date; (ii) the first
payment to the Executive under the Retirement Plan will be made on the first
day of the month on or next following the later of the Executive's 60th
Birthday or the Severance Date; and (iii) the Executive will live to the
payment date described in the preceding clause (ii).

         1.16    Service:  The number of the Executive's completed months of
continuous employment with the Employer ending on the Executive's Severance 
Date.

         1.17    Service Factor:  If the Executive has 240 or more months of
Service then the Service Factor shall equal one (l).  At any time prior to the
time when the Executive has both earned a vested benefit under the Retirement
Plan and been continuously employed by an Employer for five years, the Service
Factor shall be 0.  Except as otherwise provided in the foregoing sentences,
the Service Factor shall be a fraction, the numerator of which shall be the
number of the Executive's months of Service and the denominator of which shall
be 240.

         1.18    Severance Date:  The earlier of (i) the first date on which
(for whatever reason) the Executive is no longer employed by an Employer, or
(ii) the date of termination of this Agreement pursuant to Article 3.

         1.19    Social Security Benefit:  The amount of the monthly benefit,
as estimated by the Committee in a consistent and uniform manner, which, under
the provisions of the federal Social Security Act as amended and in effect on
the Severance Date, such Executive is, or will be, entitled to receive as the
Executive's "primary insurance amount" or any portion thereof at the later of
the Eligibility Date or the Normal Retirement Date assuming (i) that the
Executive has or will make appropriate and timely application for such benefit,
(ii) that no event has occurred or will occur by reason of which the amount of
such benefit has been or will be delayed, suspended or forfeited in whole or in
part, (iii) that if the Severance Date occurs prior to the Executive's 60th
Birthday, the Executive will continue to receive, until the Executive's 60th
Birthday, earnings at the Compensation rate taxable as wages by the Social
Security Act, and (iv) that, after the later to occur of the Executive's 60th
birthday or Normal Retirement Date, the Executive will have no further earnings
taxable as wages by the Social Security Act.

         1.20    Spouse:  The spouse to whom the Executive was married at the
date of the Executive's death and throughout the twelve-month period preceding
the Executive's Severance Date.

         1.21    Supplemental Retirement Benefit:  The benefit described in 
Section 2.2.

         1.22    Supplemental Spouse's Retirement Benefit:  The benefit
described in Section 2.3.





                                       3
<PAGE>   4

         1.23    The masculine gender shall be deemed to include the feminine;
the feminine to include the masculine; the singular to include the plural; and
the plural to include the singular in each case where appropriate.

                             ARTICLE 2 -- BENEFITS

         2.1     Eligibility.  The Executive and Spouse, as applicable, shall
be entitled to the benefits described in Sections 2.2 and 2.3; provided, that
no benefits shall be paid under this Agreement if (i) the Executive's
employment by an Employer is terminated for Cause, or (ii) the Severance Date
occurs for any reason before the Executive has both earned a vested benefit
under the Retirement Plan and been continuously employed by an Employer for
five years.

         2.2     Supplemental Retirement Benefit.  Subject to the other
provisions of this Agreement, commencing on the Executive's Normal Retirement
Date the Executive shall be entitled to receive a Supplemental Retirement
Benefit, which shall be payable monthly during the Executive's life with the
last payment being the payment made or due for the month in which the Executive
dies.  No benefit shall be payable under this Section 2.2 if the Executive dies
on or before the Normal Retirement Date.

                 The Supplemental Retirement Benefit shall be an amount equal
to the product of "A" multiplied by the Service Factor.  With respect to
Supplemental Retirement Benefit payments made for periods commencing prior to
the Eligibility Date, "A" shall equal the amount by which 60% of Compensation
exceeds the Retirement Plan Benefit.  With respect to Supplemental Retirement
Benefit payments made for periods commencing on or after the Eligibility Date,
"A" shall equal the amount by which 60% of Compensation exceeds the sum of the
Retirement Plan Benefit plus the Social Security Benefit.

                 If the Executive terminates employment due to Disability, (i)
the period that the Executive receives disability benefits from a disability
program sponsored or maintained by an Employer shall be treated as Service, and
(ii) the Supplemental Retirement Benefit shall not commence, and the Executive
shall not be deemed to have had a Severance Date, while the Executive is
receiving disability benefits payable from a disability program sponsored or
maintained by an Employer.  For purposes of this Section 2.2, reclassification
under the Retirement Plan from Disability Retirement to Retirement shall
constitute cessation of disability benefits.

         2.3     Supplemental Spouse's Retirement Benefit.

                 (a)      Subject to the other provisions of this Agreement,
following the Executive's death the surviving Spouse shall be entitled to a
Supplemental Spouse's Retirement Benefit, which shall be payable monthly
commencing on the later of (i) the first day of the month following the month
of the Executive's death or (ii) the first day of the month of the Executive's
55th Birthday, and continuing until the Spouse's death.  The Supplemental
Spouse's Retirement Benefit shall be an amount equal to 50% of the monthly
Supplemental Retirement Benefit which the Executive would have been entitled to
receive had death not occurred (based on Service through the





                                       4
<PAGE>   5

Severance Date and adjusting on the Eligibility Date); provided that if the
Executive's death occurs after the Severance Date, for each of the first three
months following the Executive's death the Supplemental Spouse's Retirement
Benefit shall be 100% of such amount.

                 (b)      If the Executive shall die while a Lump Sum Election
is in effect and while the Executive is still employed by the Employer, the
surviving Spouse shall receive in lieu of the benefit described in Section
2.3(a) above, a lump sum payment equal to one-half of the Present Value of the
Supplemental Retirement Benefit which the Executive would have been entitled to
receive based on Service through the Severance Date if the Executive had
survived to the Normal Retirement Date.  Such benefit shall be paid as promptly
as practicable after the Executive's death and, in all events, within
forty-five (45) days after the Executive's death.  For purposes of this Section
2.3(b), the determination of whether a Spouse has survived the Executive shall
be made in accordance with the provisions of Section 43-8-43 of the Code of
Alabama of 1975, as the same may from time to time be amended (as of the date
of this Agreement, Section 43-8-43 generally treats a person as having
predeceased a decedent unless the person survives the decedent by five days).

                 (c)      If the Executive shall die after the Severance Date,
while a Lump Sum  Election is in effect, and prior to receipt of the lump sum
payment, the lump sum benefit shall be payable to the Executive's estate and no
Supplemental Spouse's Retirement Benefit shall be payable to the surviving
Spouse, if any.

                 (d)      If the Executive dies after payment of a lump sum
pursuant to Section 2.5, no Supplemental Spouse's Retirement Benefit shall be
payable to the Executive's surviving Spouse, if any.

                 (e)      No benefit shall be payable following the Executive's
death except as provided in this Section 2.3.

         2.4     Spouse's Age.  If a Spouse who is entitled to a benefit under
this Article 2 is more than ten (10) years younger than the Executive, any
benefit payable to the Spouse under Section 2.3(a) (but not 2.3(b)) shall be
reduced by 1/20 for each full year of age difference more than ten (10).

         2.5     Payment Elections.

                          (a)     By checking the appropriate box on the
signature page of this Agreement, the Executive may elect to receive, in lieu
of the Supplemental Retirement Benefit to which the Executive will otherwise
become entitled under Section 2.2 hereof, a lump sum payment that is the
Present Value, as of the date payment is made, of such Supplemental Retirement
Benefit.  Such payment shall be made as promptly as practicable after the
Executive's Severance Date and, in all events, within forty-five (45) days
after such Severance Date.

                          (b)     By executing and filing with the Company a
form substantially identical to Exhibit I hereof, or such other form as the
Company may prescribe or approve, the





                                       5
<PAGE>   6

Executive may revoke an election made pursuant to paragraph (a) above or may
make any election which could be made pursuant to such paragraph, but any such
election or revocation of an election shall not become effective if the
Executive's Severance Date occurs within one year from the date such revocation
or election is made.


         2.6     Leave of Absence.  In the event the Executive is granted a
leave of absence, the Executive's employment shall be deemed to continue and
shall be treated as Service, during the period of such leave of absence unless
specifically determined to the contrary by the Committee.


              ARTICLE 3 -- AMENDMENT OR TERMINATION OF AGREEMENT

         3.1     Subject to Section 3.2 below, the Company reserves the right
to terminate this Agreement at any time by action of its Board of Directors or
the Committee, and the continuance of this Agreement is not guaranteed to the
Executive.

         3.2     No termination of this Agreement shall operate to reduce,
cancel or void the Company's obligation to pay benefits provided for under this
Agreement and accrued prior to the Severance Date.

         3.3     This Agreement may be amended by written instrument executed
by the Executive and by an officer of the Company thereunto duly authorized by
the Board of Directors of the Company.


                          ARTICLE 4 -- MISCELLANEOUS

         4.1     This Agreement shall under no circumstances be deemed to have
any effect upon the terms or conditions of employment of the Executive.  The
establishment and maintenance of this Agreement shall not be construed as
creating or modifying any contract between an Employer and the Executive nor is
it in lieu of any other benefits.  This Agreement shall under no circumstances
be deemed to constitute a contract of insurance.

         4.2     This Agreement shall not give the Executive the right to be
retained in the employ of an Employer or any right or interest hereunder other
than as specifically provided herein.

         4.3     Benefits under this Agreement shall not be subject in any
manner to anticipation, alienation, sale, transfer, assignment, pledge or
encumbrance by the Executive or the Spouse and any attempt to so transfer or
encumber the benefits shall be null and void.  Benefits under this Agreement
shall not be subject to or liable for the debts, contracts, liabilities,
engagements or torts of the Executive or of the Spouse nor may the same be
subject to attachment or seizure by any creditor of the Executive or the
Executive's spouse under any circumstances.





                                       6
<PAGE>   7

         4.4     In the event of the Executive's Retirement, Disability or
death, the Executive or the Executive's Spouse, as the case may be, should
notify the Committee promptly, and the Committee will then provide a Claimant's
statement form for completion which should be returned to the Committee
together with evidence of Disability or with an official death certificate, if
applicable.  In the event that any claim hereunder is denied, the Committee
will provide adequate notice in writing to the Executive or Spouse, setting
forth the specific reasons for such denial and, in addition, the Committee will
afford a reasonable opportunity for a full and fair review of those reasons.

                 IN WITNESS WHEREOF, the Company has caused this Agreement to
be executed by its duly authorized officer and the Executive has hereunto set
his/her hand and seal all as of the day and year first above written.

                                                  ENERGEN CORPORATION


                                        By:
                                            ------------------------------------
                                        Its:
                                             -----------------------------------


                                        EXECUTIVE



                                        ----------------------------------------


                                        ELECTION

         [ ]     I hereby elect to have my benefit paid as provided in Section
                 2.2 of this Agreement.

         [ ]     Pursuant to Section 2.5 of this Agreement, I hereby elect to
                 have my benefit paid in a lump sum.





                                       7
<PAGE>   8
                                   EXHIBIT I

                                    ELECTION
                                  PURSUANT TO
                   EXECUTIVE RETIREMENT SUPPLEMENT AGREEMENT


                 I hereby revoke any and all elections heretofore made by me
pursuant to the terms of that certain Executive Retirement Supplement Agreement
entered into by and between Energen Corporation and myself dated as of
________________, and elect to have my benefit

                 [ ]      paid as provided in Section 2.2 of such Agreement.

                 [ ]      paid in a lump sum pursuant to Section 2.5 of such
                          Agreement.

                 I understand that the foregoing election (and revocation, if
applicable), will not become effective if my Severance Date occurs within
one-year from the date of acceptance indicated below.


                                        ----------------------------------------
                                                 EXECUTIVE

                                        ----------------------------------------
                                                
                                        Accepted by:
                                        ENERGEN CORPORATION


                                        ----------------------------------------
                                        By:
                                              ----------------------------------
                                        Its:
                                              ----------------------------------
                                        Date:
                                              ----------------------------------




                                       8