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                                                                     EXHIBIT 4.1









                             SOUTHWEST AIRLINES CO.

                               EXCESS BENEFIT PLAN










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                             SOUTHWEST AIRLINES CO.

                               EXCESS BENEFIT PLAN


                                Table of Contents




                                                                                                                Page
                                                                                                                ----
                                                                                                              
ARTICLE I           DEFINITIONS...................................................................................1

ARTICLE II          ELIGIBILITY...................................................................................2

ARTICLE III         CREDITS TO ACCOUNT............................................................................3

ARTICLE IV          BENEFITS......................................................................................4

ARTICLE V           PAYMENT OF BENEFITS...........................................................................4

ARTICLE VI          IN-SERVICE WITHDRAWALS AND LOANS..............................................................5

ARTICLE VII         ADMINISTRATION OF THE PLAN....................................................................7

ARTICLE VIII        LIMITATION OF RIGHTS..........................................................................8

ARTICLE IX          LIMITATION OF ASSIGNMENT AND PAYMENTS TO
                    LEGALLY INCOMPETENT DISTRIBUTEE...............................................................8

ARTICLE X           AMENDMENT TO OR TERMINATION OF THE PLAN.......................................................9

ARTICLE XI          STATUS OF PARTICIPANT AS UNSECURED CREDITOR...................................................9

ARTICLE XII         GENERAL AND MISCELLANEOUS.....................................................................9





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                             SOUTHWEST AIRLINES CO.
                               EXCESS BENEFIT PLAN


                                    PREAMBLE

         WHEREAS, Southwest Airlines Co., a corporation formed under the laws of
the State of Texas, desires to establish an excess benefit plan for the
exclusive benefit of its employees to restore retirement benefits decreased due
to limitations imposed by Section 415 of the Internal Revenue Code of 1986; and

         WHEREAS, Southwest Airlines Co. intends that any Participant or
Beneficiary under the Plan shall have the status of an unsecured general
creditor with respect to the Plan and any Trust Fund;

         NOW, THEREFORE, Southwest Airlines Co. hereby establishes the Southwest
Airlines Co. Excess Benefit Plan, effective January 1, 1999.


                                    ARTICLE I

                                   DEFINITIONS

         1.1 "Account" shall mean the record maintained by the Committee showing
the monetary value of the individual interest in the Plan of each Participant or
Beneficiary. The term "Account" shall refer only to a bookkeeping entry and
shall not be construed to require the segregation of assets on behalf of any
Participant or Beneficiary.

         1.2 "Beneficiary" shall mean, with respect to each Participant, the
beneficiary of such Participant under the Southwest Airlines Co. ProfitSharing
Plan.

         1.3 "Board" shall mean the Board of Directors of Southwest Airlines Co.

         1.4 "Code" shall mean the Internal Revenue Code of 1986, as it may be
amended from time to time, and the rules and regulations promulgated thereunder.

         1.5 "Committee" shall mean the committee designated by the Board to
administer the Plan.

         1.6 "Company" shall mean Southwest Airlines Co., or its successor or
successors.

         1.7      "Effective Date" shall mean January 1, 1999.

         1.8 "Excess Amount" shall mean, for a particular Plan Year, the amount
by which the allocation(s) of a Participant under the Retirement Plans which are
attributable to such Plan Year are reduced by reason of the application of the
limitations set forth in Section 415 of the Code.






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         1.9 "Mandatory Retirement Age" shall, with respect to each Southwest
Airlines Co. pilot, mean the mandatory retirement age, if any, imposed by the
Federal Aviation Agency.

         1.10 "Participant" shall mean an Employee who has met the eligibility
requirements for participation in this Plan, as set forth in Article II hereof.

         1.11 "Plan" shall mean the Southwest Airlines Co. Excess Benefit Plan,
as set forth in this document, and as amended from time to time.

         1.12 "Plan Year" shall mean the annual period beginning on January 1
and ending on December 31, both dates inclusive of each year.

         1.13 "Retirement Plans" shall mean the Southwest Airlines Co.
ProfitSharing Plan (the "ProfitSharing Plan"), the Southwest Airlines Co. 401(k)
Plan and the Southwest Airlines Co. Pilots' Retirement Savings Plan.

         1.14 "Trust Agreement" shall mean the agreement, if any, including any
amendments thereto, entered into between the Company and the Trustee to carry
out the provisions of the Plan.

         1.15 "Trust Fund" shall mean the cash and other properties held and
administered by the Trustee pursuant to the Trust Agreement.

         1.16 "Trustee" shall mean the designated trustee acting at any time
under the Trust Agreement.

         1.17 "Valuation Date" shall mean each business day on which the
financial markets are open for trading activity.


                                   ARTICLE II

                                   ELIGIBILITY

         Each employee of the Company who qualifies for an allocation under each
or any one of the Retirement Plans, the amount of which is reduced by reason of
the application of the limitations set forth in Section 415 of the Code,
resulting in an Excess Amount, shall automatically be eligible to participate in
this Plan.





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                                   ARTICLE III

                               CREDITS TO ACCOUNT

         3.1 For each Plan Year, as soon as practicable following the date on
which the Company funds its contribution, if any, to the ProfitSharing Plan, the
Company shall credit to the Account of each Participant who is actively employed
on the date on which such ProfitSharing contribution is funded, an amount equal
to the Excess Amount of such Participant for the preceding Plan Year.

         3.2 As of each Valuation Date, the Committee shall credit to each
Participant's Account the deemed income or losses attributable thereto, as
provided in Section 3.3 below, as well as any other credits to or charges
against such Account, including such Participant's pro rata portion of Plan
administrative expenses. All payments from an Account between Valuation Dates
shall be charged against the Account as of the preceding Valuation Date.

         3.3 Each Participant, prior to initial participation in the Plan, may,
in the manner prescribed by the Committee, designate the manner in which amounts
credited to such Participant's Account pursuant to Section 3.1 above shall be
deemed to be invested among the various options designated by the Committee for
this purpose. Such designation may be changed as of any Valuation Date solely
with respect to amounts credited under Section 3.1 after the date of such
change, and shall be effected by filing an election with the Committee, in the
manner prescribed by the Committee, within the period of time prior to such
Valuation Date established by the Committee. The Participant must designate, in
such minimum percentages or amounts as may be prescribed by the Committee, that
portion of the amount to be credited to the Account of such Participant which is
to be allocated to each investment option offered hereunder. In the absence of
any such investment designation, amounts credited to a Participant's Account
shall be deemed to be invested in such property as the Committee, in its sole
and absolute discretion, shall determine. In no event may any Participant
designate the investment of amounts credited to an Account in stock or other
securities of the Company. The Committee may, but shall not be obligated to,
invest amounts credited to a Participant's Account in accordance with the
investment designations of such Participant; nevertheless, the Account of such
Participant shall be credited with the amount of income, gains and losses
attributable thereto, as if the amounts credited to such Account had been so
invested. The Committee shall be authorized at any time and from time to time to
modify, alter, delete or add to the investment options hereunder. In the event a
modification occurs, the Committee shall, prior to the effective date of such
change, notify those Participants whom the Committee, in its sole and absolute
discretion, determines are affected by the change. The Committee shall not be
obligated to substitute options with similar investment criteria for existing
options, nor shall it be obligated to continue the types of investment options
presently available to the Participants.





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                                   ARTICLE IV

                                    BENEFITS

         4.1 Upon the death of a Participant, the Beneficiary of such
Participant shall be entitled to the entire value of all amounts credited to
such Participant's Account, as of the Valuation Date coincident with or
preceding the date of distribution.

         4.2 Upon a Participant's termination of employment or, if earlier,
attainment of Mandatory Retirement Age, as applicable, such Participant shall be
entitled to the entire value of all amounts credited to the Account of such
Participant, as of the Valuation Date coincident with or preceding the date of
distribution.


                                    ARTICLE V

                               PAYMENT OF BENEFITS

         5.1 Payment of a Participant's benefit on account of the attainment of
Mandatory Retirement Age or termination of employment shall be made either in a
lump sum in cash, or in cash payments in annual installments over a period
certain not exceeding five (5) years, such method of payment to be irrevocably
elected by the Participant upon initial participation in the Plan in the manner
prescribed by the Committee; provided, however, that payment will be made in a
lump sum in any event if, at the time distribution of the Account is to
commence, the amount credited to the Account is $25,000 or less. Furthermore,
notwithstanding the commencement of installment payments under this Section 5.1,
all remaining amounts credited to a Participant's Account shall be distributed
in a lump sum in cash, at such time as the value of such remaining amounts is
$25,000 or less. Payment shall commence at the time specified by the Participant
upon initial participation in the Plan, which may be as soon as practicable
following the Participant's termination of employment with the Company or, if
earlier, attainment of Mandatory Retirement Age, if applicable, and during the
calendar year in which such event occurs or, if so elected by the Participant,
as soon as practicable during the calendar year following the year in which such
event occurs. If installment payments are made, such payments shall be charged
pro rata to the individual investment options in which amounts credited to the
Participant's Account are deemed to be invested, pursuant to the Participant's
designation under Section 3.3 hereof. Furthermore, the Committee shall continue
to credit the unpaid balance of the Participant's Account with the deemed income
and losses attributable thereto, in accordance with such Participant's elections
pursuant to the provisions of Section 3.3 hereof, as well as with any other
credits to or charges against the unpaid balance of such Account, during the
period for which installment payments are made.

         5.2 Payment of a Participant's benefit on account of death shall be
made in a lump sum in cash. Payment of a Participant's death benefit shall be
made to the Beneficiary of such Participant as soon as practicable following the
Committee's receipt of proper notice of such Participant's death.



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         5.3 Notwithstanding any other provision herein to the contrary, unless
a Participant elects, prior to the beginning of any Plan Year, in the manner and
at the time prescribed by the Committee, to defer the receipt of all or a
portion of the amount to be credited to the Account of such Participant
hereunder for such Plan Year pursuant to Section 3.1 hereof, such amount shall
be paid to such Participant in a cash lump sum as soon as practicable after such
amount is credited to such Participant's Account. Any election to defer the
receipt of all or a portion of the amount credited in accordance with Section
3.1 shall be permitted only if the portion deferred equals or exceeds $1,000.
Any such election shall be effective for all subsequent Plan Years, unless prior
to the beginning of a Plan Year, the Participant affirmatively changes such
election in the manner prescribed by the Committee.

         5.4 Notwithstanding the provisions of sections 5.1 or 5.2, the benefits
payable hereunder may be paid before they would otherwise be payable if, based
on a change in the federal or applicable state tax or revenue laws, a published
ruling or similar announcement issued by the Internal Revenue Service, a
regulation issued by the Secretary of the Treasury, a decision by a court of
competent jurisdiction involving a Participant or a Beneficiary, or a closing
agreement made under Section 7121 of the Code that is approved by the Internal
Revenue Service and involves a Participant, the Committee determines that a
Participant has or will recognize income for federal or state income tax
purposes with respect to amounts that are or will be payable under the Plan
before they otherwise would be paid. The amount of any payments pursuant to this
Section 5.4 shall not exceed the lesser of: (a) the amount in the Participant's
Account or (b) the amount of taxable income with respect to which the tax
liability is assessed or determined.

         5.5 The payment of benefits under the Plan shall begin at the date
specified in accordance with the provisions of Sections 5.1, 5.2 and 5.3 hereof;
provided that, in case of administrative necessity, the starting date of payment
of benefits may be delayed up to thirty (30) days as long as such delay does not
result in the Participant or Beneficiary receiving the distribution in a
different taxable year than if no such delay had occurred.


                                   ARTICLE VI

                        IN-SERVICE WITHDRAWALS AND LOANS

         6.1 In the event of an unforeseeable emergency, a Participant may make
a request to the Committee for a withdrawal from the Account of such
Participant. For purposes of this Section, the term "unforeseeable emergency"
shall mean a severe financial hardship to the Participant resulting from a
sudden and unexpected illness or accident of the Participant or of a dependent
(as defined in Section 152(a) of the Code) of the Participant, loss of the
Participant's property due to casualty, or other similar extraordinary and
unforeseeable circumstances arising as a result of events beyond the control of
the Participant. Any determination of the existence of an unforeseeable
emergency and the amount to be withdrawn on account thereof shall be made by the
Committee, in its sole and absolute discretion. However, notwithstanding the
foregoing, a withdrawal will not be permitted



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to the extent that the financial hardship is or may be relieved: (i) through
reimbursement or compensation by insurance or otherwise; (ii) by liquidation of
the Participant's assets, to the extent that liquidation of such assets would
not itself cause severe financial hardship; or (iii) by cessation of deferrals
under this Plan. In no event shall the need to send a Participant's child to
college or the desire to purchase a home be deemed to constitute an
unforeseeable emergency. No member of the Committee shall vote or decide upon
any matter relating to the determination of the existence of such member's own
financial hardship or the amount to be withdrawn on account thereof. A request
for a hardship withdrawal must be made in the manner prescribed by the
Committee, and must be expressed as a specific dollar amount. The amount of a
hardship withdrawal may not exceed the amount required to meet the severe
financial hardship. All hardship withdrawals shall be paid in a lump sum in
cash.

         6.2 A Participant may, prior to the beginning of any Plan Year, in the
manner prescribed by the Committee, request an in-service withdrawal of all or a
portion of any amounts which have been credited to the Account of such
Participant pursuant to Section 3.1 above for at least three (3) calendar years
as of the beginning of such Plan Year, together with any income attributable
thereto; provided, however, that the amount of any such withdrawal shall never
exceed such credited amounts, as adjusted for any deemed income or losses
attributable thereto. Such request must set forth the specific dollar amount to
be withdrawn and the time at which payment is to be made. The Committee, in its
sole and absolute discretion, shall, upon review of the facts pertinent to such
request, determine whether the withdrawal request shall be approved. No member
of the Committee shall vote upon, decide, or participate in any other way in a
decision involving a withdrawal request of such Committee member. Any withdrawal
under this Section 6.2 shall be made in a single lump sum, in cash.

         6.3 Notwithstanding any other provision herein to the contrary, a
Participant may elect at any time, in the manner prescribed by the Committee, to
accelerate the date on which payment of such Participant's benefit hereunder
would otherwise be made. Upon such election, the amount to which such
Participant is entitled shall be ninety percent (90%) of the benefit otherwise
payable hereunder, which shall be distributed in one lump sum, in cash, as soon
as administratively practicable following such election.

         6.4 Withdrawals shall be charged pro rata to the individual investment
options in which amounts credited to a Participant's Account are deemed to be
invested, pursuant to such Participant's designation under Section 3.3 hereof.

         6.5 In no event may a Participant receive a loan of any portion of his
benefit hereunder.





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                                   ARTICLE VII

                           ADMINISTRATION OF THE PLAN

         7.1 The Committee may establish a Trust Fund for the purpose of
retaining assets set aside by the Company pursuant to the Trust Agreement for
payment of all or a portion of the benefits payable pursuant to the Plan. Any
benefits not paid from a Trust shall be paid from the Company's general assets.
The Trust Fund, if such shall be established, shall be subject to the claims of
general creditors of the Company in the event the Company is Insolvent, as such
term is defined in the Trust Agreement.

         7.2 The Plan shall be administered by the Committee. The members of the
Committee shall not receive compensation with respect to their services for the
Committee. The members of the Committee shall serve without bond or security for
the performance of their duties hereunder unless applicable law makes the
furnishing of such bond or security mandatory or unless required by the Company.
Any member of the Committee may resign by delivering a written resignation to
the Company and to the other members of the Committee.

         7.3 The Committee shall perform any act which the Plan authorizes
expressed by a vote at a meeting or in a writing signed by a majority of its
members without a meeting. The Committee may, by a writing signed by a majority
of its members, appoint any member of the Committee to act on behalf of the
Committee. Any person who is a member of the Committee shall not vote or decide
upon any matter relating solely to such member or vote in any case in which the
individual right or claim of such member to any benefit under the Plan is
particularly involved. If, in any matter or case in which a person is so
disqualified to act, the remaining persons constituting the Committee cannot
resolve such matter or case, the Board will appoint a temporary substitute to
exercise all the powers of the disqualified person concerning the matter or case
in which such person is disqualified.

         7.4 The Committee may designate in writing other persons to carry out
its responsibilities under the Plan, and may remove any person designated to
carry out its responsibilities under the Plan by notice in writing to that
person. The Committee may employ persons to render advice with regard to any of
its responsibilities. All usual and reasonable expenses of the Committee shall
be paid by the Company. The Company shall indemnify and hold harmless each
member of the Committee from and against any and all claims and expenses
(including, without limitation, attorney's fees and related costs), in
connection with the performance by such member of duties in that capacity, other
than any of the foregoing arising in connection with the willful neglect or
willful misconduct of the person so acting.

         7.5 The Committee shall establish rules and procedures, not contrary to
the provisions of the Plan, for the administration of the Plan and the
transaction of its business. The Committee shall determine the eligibility of
any individual to participate in the Plan, shall interpret the Plan in its sole
and absolute discretion, and shall determine all questions arising in the
administration, interpretation and application of the Plan. All determinations
of the Committee shall be conclusive



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and binding on all employees, Participants and Beneficiaries, subject to the
provisions of this Plan and applicable law.

         7.6 Any action to be taken hereunder by the Company shall be taken by
resolution adopted by the Board or by a committee thereof; provided, however,
that by resolution, the Board or a committee thereof may delegate to any officer
of the Company the authority to take any such actions hereunder, other than the
power to amend or terminate the Plan.


                                  ARTICLE VIII

                              LIMITATION OF RIGHTS

         The establishment of this Plan shall not be construed as giving to any
Participant, employee of the Company or any person whomsoever, any legal,
equitable or other rights against the Company, or its officers, directors,
agents or shareholders, or as giving to any Participant or Beneficiary any
equity or other interest in the assets or business of the Company or shares of
Company stock or as giving any employee the right to be retained in the
employment of the Company. All employees of the Company and Participants shall
be subject to discharge to the same extent they would have been if this Plan had
never been adopted. The rights of a Participant hereunder shall be solely those
of an unsecured general creditor of the Company.


                                   ARTICLE IX

                    LIMITATION OF ASSIGNMENT AND PAYMENTS TO
                         LEGALLY INCOMPETENT DISTRIBUTEE

         9.1 No benefits which shall be payable under the Plan to any person
shall be subject in any manner to anticipation, alienation, sale, transfer,
assignment, pledge, encumbrance or charge, and any attempt to anticipate,
alienate, sell, transfer, assign, pledge, encumber, charge or otherwise dispose
of the same shall be void. No benefit shall in any manner be subject to the
debts, contracts, liabilities, engagements or torts of any person, nor shall it
be subject to attachment or legal process for or against any person, except to
the extent required by law.

         9.2 Whenever any benefit which shall be payable under the Plan is to be
paid to or for the benefit of any person who is then a minor or determined by
the Committee, on the basis of qualified medical advice, to be incompetent, the
Committee need not require the appointment of a guardian or custodian, but shall
be authorized to cause the same to be paid over to the person having custody of
the minor or incompetent, or to cause the same to be paid to the minor or
incompetent without the intervention of a guardian or custodian, or to cause the
same to be paid to a legal guardian or custodian of the minor or incompetent, if
one has been appointed, or to cause the same to be used for the benefit of the
minor or incompetent.



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                                    ARTICLE X

                     AMENDMENT TO OR TERMINATION OF THE PLAN

         The Company reserves the right at any time to amend or terminate the
Plan in whole or in part by resolution of the Board. No amendment shall have the
effect of retroactively changing or depriving Participants or Beneficiaries of
rights already accrued under the Plan. Upon termination of the Plan, the Board
may, in its sole and absolute discretion, and notwithstanding any other
provision hereunder to the contrary, direct that all benefits hereunder will be
paid as soon as administratively practicable thereafter.


                                   ARTICLE XI

                   STATUS OF PARTICIPANT AS UNSECURED CREDITOR

         All benefits under the Plan shall be the unsecured obligations of the
Company and, except for those assets which may be placed in a Trust Fund
established in connection with this Plan, no assets will be placed in trust or
otherwise segregated from the general assets of the Company for the payment of
obligations hereunder. To the extent that any person acquires a right to receive
payments hereunder, such right shall be no greater than the right of any
unsecured general creditor of the Company.


                                   ARTICLE XII

                            GENERAL AND MISCELLANEOUS

         12.1 Severability. In the event that any provision of this Plan shall
be declared illegal or invalid for any reason, said illegality or invalidity
shall not affect the remaining provisions of this Plan but shall be fully
severable and this Plan shall be construed and enforced as if said illegal or
invalid provision had never been inserted herein.

         12.2 Construction. The Section headings and numbers are included only
for convenience of reference and are not to be taken as limiting or extending
the meaning of any of the terms and provisions of this Plan. Whenever
appropriate, words used in the singular shall include the plural or the plural
may be read as the singular.

         12.3 Governing Law. The validity and effect of this Plan and the rights
and obligations of all persons affected hereby shall be construed and determined
in accordance with the laws of the State of Texas unless superseded by federal
law.




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         12.4 No Requirement to Fund. The Company is not required to set aside
any assets for payment of the benefits provided under this Plan; however, it may
do so as provided in the Trust Agreement, if any. A Participant shall have no
security interest in any such amounts. It is the Company's intention that this
Plan be construed as a plan which is unfunded and maintained primarily for the
purpose of providing deferred compensation for a select group of highly
compensated employees.

         12.5 Taxes. All amounts payable hereunder shall be reduced by any and
all federal, state and local taxes imposed upon the Participant or a Beneficiary
which are required to be paid or withheld by the Company.

         IN WITNESS WHEREOF, Southwest Airlines Co., the Company, has caused its
corporate seal to be affixed hereto and these presents to be duly executed in
its name and behalf by its proper officers thereunto duly authorized this
20th day of November, 1998.


                                             COMPANY:

                                             SOUTHWEST AIRLINES CO.



                                             By: /s/ Herbert D. Kelleher
                                                 ------------------------------

ATTEST:

/s/ Colleen C. Barrett
- ----------------------------------
                          (Title)

[CORPORATE SEAL]


155:12479-5