<PAGE>   1
                                                                  EXHIBIT 10.H.1

                                AMENDMENT TO THE
                                   SONAT INC.
                            SUPPLEMENTAL BENEFIT PLAN

         El Paso Energy Corporation, a Delaware corporation ("El Paso"), as
successor to Sonat Inc., a Delaware corporation ("Sonat"), does hereby amend the
Sonat Inc. Supplemental Benefit Plan (the "Plan") as set forth below:

         WHEREAS, on October 25, 1999, Sonat merged with and into El Paso
pursuant to the terms of the Merger Agreement (as defined below); and

         WHEREAS, El Paso, as successor to Sonat and pursuant to Section 6.10(a)
of the Merger Agreement, has assumed all of Sonat's obligations under the Plan;
and

         WHEREAS, the Merger was a Change of Control (as defined in the Plan);
and

         WHEREAS, El Paso desires to amend the Plan and to provide for the
merger of the Plan into the El Paso Supplemental Plan (as defined below).

         NOW, THEREFORE, the following Plan provisions are hereby adopted:

         1.       A new Article VIII is added to the Plan after Article VII,
                  such new Article VIII to read in its entirety as follows:

                       ARTICLE VIII - EL PASO MERGER PROVISIONS

                  8.1      DEFINITIONS

                  The following terms shall have the following meaning, unless
                  the context clearly indicates otherwise:

                  EL PASO DEFERRED COMPENSATION PLAN shall mean the El Paso
                  Energy Corporation Deferred Compensation Plan, as from time to
                  time amended.

                  EL PASO SUPPLEMENTAL PLAN shall mean the El Paso Energy
                  Corporation Supplemental Benefits Plan, as from time to time
                  amended.

                  MERGER shall mean the merger of Sonat Inc. with and into El
                  Paso Energy Corporation pursuant to the Merger Agreement.

                  MERGER AGREEMENT shall mean the Second Amended and Restated
                  Agreement and Plan of Merger dated as of March 13, 1999 (as
                  amended from time to time) by and between Sonat Inc. and El
                  Paso Energy Corporation.


                                       1
<PAGE>   2
                  MERGER EFFECTIVE TIME shall mean the Effective Time of the
                  Merger, as determined pursuant to the Merger Agreement.

                  WINDOW PROGRAM shall mean the Early Retirement Window Program
                  offered in connection with the Merger.

                  8.2      EXCESS CASH BALANCE BENEFITS

                           (a)      In no event will credits be made to a
                                    Participant's Cash Balance Account under
                                    Section 5.2(a) with respect to pay periods
                                    beginning after December 31, 1999.

                           (b)      The Cash Balance Account of a Participant
                                    who has a Termination of Employment before
                                    January 1, 2000, shall be paid as provided
                                    under the terms of the Plan as in effect
                                    immediately before the Merger Effective
                                    Time.

                           (c)      The Cash Balance Account of a Participant
                                    who does not have a Termination of
                                    Employment before January 1, 2000, shall be
                                    paid on the earlier of (a) the date that is
                                    30 days following the Participant's
                                    Termination of Employment (or, if such date
                                    is not a business day, on the preceding
                                    business day) and (b) March 31, 2000. All
                                    payments made pursuant to this Section
                                    8.2(c) shall be calculated as provided in
                                    Sections 5.2(b) and 5.3.

                  8.3      EXCESS SAVINGS PLAN BENEFITS

                           (a)      In no event will credits be made to
                                    Participant's Accounts under Section 3.2(a)
                                    with respect to pay periods beginning after
                                    December 31, 1999.

                           (b)      The Accounts of a Participant who has a
                                    Termination of Employment before January 1,
                                    2000, shall be paid in accordance with the
                                    provisions of the Plan as in effect
                                    immediately before the Merger Effective
                                    Time.

                           (c)      The Accounts of a Participant in the Plan
                                    who is not a "Participant" in the El Paso
                                    Supplemental Plan on January 1, 2000, shall
                                    be paid in a cash lump sum on March 31,
                                    2000, regardless of whether the Participant
                                    has had a Termination of Employment. All
                                    payments made pursuant to this Section
                                    8.3(c) shall be calculated as provided in
                                    Section 3.4(a), using a "Lump Sum Valuation
                                    Date" of March 16, 2000.



                                       2
<PAGE>   3

                           (d)      The Account of a SODI Employee shall be paid
                                    in a cash lump sum on March 31, 2000,
                                    regardless of whether the SODI Employee has
                                    had a Termination of Employment. All
                                    payments made pursuant to this Section
                                    8.3(d) shall be calculated as provided in
                                    Section 3.8(b), with interest accrued
                                    through the date of the payment.

                           (e)      The Accounts of a Participant in the Plan
                                    who is a "Participant" in the El Paso
                                    Supplemental Plan on January 1, 2000, shall
                                    be credited to the Participant's "Memorandum
                                    Account" in the El Paso Deferred
                                    Compensation Plan, as more fully provided
                                    for in the El Paso Supplemental Plan and El
                                    Paso Deferred Compensation Plan.

                  8.4      EXCESS RETIREMENT PLAN BENEFITS

                           (a)      Except as provided in Sections 8.4(d) and
                                    8.4(e), in no event will a Participant
                                    accrue Excess Retirement Plan Benefits with
                                    respect to service performed after December
                                    31, 1999.

                           (b)      Excess Retirement Plan Benefits with respect
                                    to participants who had a Termination of
                                    Employment before the Merger Effective Time
                                    shall continue to be paid in accordance with
                                    the provisions of the Plan as in effect
                                    immediately before the Merger Effective
                                    Time.

                           (c)      The Excess Retirement Plan Benefits of (1) a
                                    Participant who has a Termination of
                                    Employment before January 1, 2000, and (2) a
                                    SODI Employee who has a Termination of
                                    Employment after December 31, 1999, shall be
                                    paid in accordance with the provisions of
                                    the Plan as in effect immediately before the
                                    Merger Effective Time.

                           (d)      The Excess Retirement Plan Benefits of a
                                    Participant who has a Termination of
                                    Employment after December 31, 1999 under the
                                    terms of the Window Program, and who is not
                                    a party to an Executive Severance Agreement
                                    or an Officer Severance Agreement with
                                    Sonat, shall be determined and paid in
                                    accordance with the provisions of the Plan
                                    as in effect immediately before the Merger
                                    Effective Time.

                           (e)      Any Plan provision to the contrary
                                    notwithstanding, a Participant in the Plan
                                    who (A) has a Termination of Employment
                                    after December 31, 1999 under the terms of


                                       3
<PAGE>   4

                                    the Window Program, and (B) is a party to an
                                    Executive Severance Agreement or an Officer
                                    Severance Agreement with Sonat, shall be
                                    entitled to Excess Retirement Plan Benefits,
                                    payable in the form of a cash lump sum,
                                    equal to the sum of:

                                    (1) the Actuarial Equivalent of the excess,
                                        if any, of (i) the amount that
                                        hypothetically would have been payable
                                        to the Participant as a Retirement
                                        Benefit under the Retirement Plan (based
                                        upon the assumption that the terms of
                                        the Retirement Plan, as in effect
                                        immediately before the Merger Effective
                                        Time, applied to the Participant through
                                        the date of the Participant's
                                        Termination of Employment) if Sections
                                        401(a)(17) and 415 of the Code were
                                        nonexistent and the provisions of the
                                        Retirement Plan incorporating the
                                        limitations contained in Sections
                                        401(a)(17) and 415 of the Code were
                                        inoperative (and assuming that the
                                        Participant elected to receive such
                                        Benefit on the earliest date permitted
                                        for the commencement of Retirement
                                        Benefits under the Retirement Plan),
                                        over (ii) the amount which
                                        hypothetically would have been payable
                                        to the Participant under the last
                                        paragraph of Section 5.1(b)(iii) of the
                                        El Paso Energy Corporation Pension Plan
                                        (the "El Paso Pension Plan") upon
                                        application of the actual terms of the
                                        El Paso Pension Plan (assuming that the
                                        Participant elected to receive such
                                        amount on the earliest date permitted
                                        for the commencement of benefits under
                                        the El Paso Pension Plan); plus

                                    (2) if the Participant has an Eligible
                                        Spouse on the date of such Termination
                                        of Employment, the Actuarial Equivalent
                                        of the excess, if any, of (i) the amount
                                        that hypothetically would have been
                                        payable to the Eligible Spouse as a
                                        Survivors Benefit under the Retirement
                                        Plan upon the death of the Participant
                                        (based upon the assumption that the
                                        terms of the Retirement Plan, as in
                                        effect immediately before the Merger
                                        Effective Time, applied to the
                                        Participant through the date of the
                                        Participant's Termination of Employment)
                                        if Sections 401(a)(17) and 415 of the
                                        Code were nonexistent and Section 7.10
                                        and the provisions of the Retirement
                                        Plan incorporating the limitations
                                        contained in Sections 401(a)(17) and 415
                                        of the Code were inoperative, over (ii)
                                        the amount which hypothetically would
                                        have been


                                       4
<PAGE>   5

                                        payable to the Eligible Spouse under the
                                        last paragraph of Section 5.1(b)(iii) of
                                        the El Paso Pension Plan upon
                                        application of the actual terms of the
                                        El Paso Pension Plan (assuming that the
                                        Participant and Eligible Spouse elected
                                        to receive benefits under such Section
                                        5.1(b)(iii) on the earliest date
                                        permitted for the commencement of
                                        benefits under the El Paso Pension
                                        Plan), with such excess to be valued as
                                        a reversionary annuity, payable
                                        immediately upon the death of the
                                        Participant, using the interest rate and
                                        mortality table set forth in Section
                                        2.3(d).

                                        The cash lump-sum payment set forth in
                                        this Section 8.4(e) shall be paid as
                                        soon as practicable (and within 30 days)
                                        after the Participant's Termination of
                                        Employment, and shall be reduced by the
                                        amount of any Severance Retirement
                                        Benefit or Severance Survivors Benefit
                                        payable under the Severance Agreement
                                        referred to above.

                           (f)      The Excess Retirement Plan Benefits of a
                                    Participant in the Plan who is an employee
                                    of El Paso or one of its subsidiaries on
                                    January 1, 2000 and who is not a
                                    "Participant" in the El Paso Supplemental
                                    Plan on January 1, 2000, shall be paid in
                                    Lump Sum Form on March 31, 2000. All
                                    payments made pursuant to this Section
                                    8.4(f) shall be calculated as provided in
                                    Sections 2.3(a) and 2.3(d), based on the
                                    assumption that the Participant had a
                                    Termination of Employment on December 31,
                                    1999, and taking into account the repeal of
                                    Code Section 415(e).

                           (g)      Upon Termination of Employment, a
                                    Participant in the Plan who is an employee
                                    of El Paso or one of its subsidiaries on
                                    January 1, 2000 and who is a "Participant"
                                    in the El Paso Supplemental Plan on January
                                    1, 2000, shall be entitled to receive
                                    supplemental pension benefits as more fully
                                    provided for in the El Paso Supplemental
                                    Plan.

                  8.5      VESTING BENEFITS

                           (a)      In no event will a Participant accrue
                                    Vesting Benefits with respect to service
                                    performed after December 31, 1999.

                           (b)      The Vesting Benefits of a Participant who
                                    has a Termination of Employment before
                                    January 1, 2000, shall


                                       5
<PAGE>   6

                                    be paid in accordance with the provisions of
                                    the Plan as in effect immediately before the
                                    Merger Effective Time.

                           (c)      The Vesting Benefits of a Participant in the
                                    Plan who is not a "Participant" in the El
                                    Paso Supplemental Plan on January 1, 2000,
                                    shall be paid as a cash lump sum on March
                                    31, 2000. All payments made pursuant to this
                                    Section 8.5(c) shall be calculated as
                                    provided in Section 4.2, based on the
                                    assumption that the Participant had a
                                    Termination of Employment on December 31,
                                    1999.

                           (d)      Upon Termination of Employment after
                                    December 31, 1999, a Participant in the Plan
                                    shall be entitled to Vesting Benefits, as
                                    more fully provided for in the El Paso
                                    Supplemental Plan.

                  8.6      GENERAL PROVISIONS

                           The provisions of this Article VIII shall apply to
                           all persons who were Participants in the Plan before
                           January 1, 2000, any other Plan provision to the
                           contrary notwithstanding.

                           Only employees of Sonat Inc. or its subsidiaries
                           before the Merger Effective Time shall be eligible to
                           be Participants in the Plan.

         IN WITNESS WHEREOF, El Paso Energy Corporation has executed this
document as of October 25, 1999.

                                          EL PASO ENERGY CORPORATION




                                          By: /s/ Joel Richards III
                                              ------------------------------
                                          Executive Vice President
                                          Human Resources and Administration


                                       6