EXHIBIT 10.1

                     SOUTHWEST AIRLINES CO.
                OUTSIDE DIRECTOR INCENTIVE PLAN

     1.  Purpose.  The purpose of this Plan is to align more closely the
interests of the Outside Directors of Southwest Airlines Co. (the "Company")
with those of the Company's shareholders and to provide the Outside Directors
with retirement income.  To accomplish this purpose, the Plan compensates each
Outside Director based on the performance of the Company's Common Stock and
defers the receipt of such compensation until after the Outside Director ceases
to be a director of the Company.

     2.  Definitions.  As used in this Plan, the following words and phrases
wherever capitalized shall have the following meanings unless the context
clearly indicates that a different meaning is intended:

         (a)  "Board" shall mean the Board of Directors of the Company.

         (b)  "Committee" shall mean the Compensation Committee of the Board.

         (c)  "Common Stock" shall mean Common Stock, par value one dollar
($1.00) per share, of the Company.

         (d)  "Company" shall mean Southwest Airlines Co.

         (e)  "Effective Date" shall mean May 16, 2001.

         (f)  "Fair Market Value" shall mean, with respect to Common Stock, the
average closing sale price of Common Stock as reported on the New York Stock
Exchange for the trading days that occur during a specified period.

         (g)  "Outside Director" shall mean a non-employee director of the
Company.

         (h)  "Performance Bonus" shall, with respect to an Outside Director,
have the meaning assigned to such term in Section 4.

         (i)  "Performance Share" shall mean a unit of value equal to the Fair
Market Value of a share of Common Stock.


         (j)  "Plan" shall mean the Southwest Airlines Co. Outside Director
Incentive Plan.

         (k)  "Service Ending Date" shall, with respect to any Outside Director,
have the meaning assigned to such term in Section 4.

     3.  Performance Shares.

         (a)  On the date of the 2002 Annual Meeting of Shareholders of the
Company, the Company shall grant 750 Performance Shares to each Outside
Director who has served as a director of the Company since at least May 2001.
Thereafter, on the date of each Annual Meeting of Shareholders beginning in
2003, the Company shall grant 750 Performance Shares to each Outside Director
who has served since the previous Annual Meeting.  No pro-rated grants shall be
made.  If a Director retires as of an Annual Meeting date, such Director shall
be awarded Performance Shares for the preceding year if he or she has so
served.

        (b)  The Company shall appropriately record each grant of Performance
Shares on its books and furnish each Outside Director with a written notice
reflecting the number of Performance Shares granted and such other terms and
conditions consistent with the Plan as the Committee shall determine.

     4.  Distribution.  On the 30th calendar day following such date (the
"Service Ending Date") as an Outside Director shall cease serving as a director
of the Company, the Company shall pay to such Outside Director an amount (the
"Performance Bonus") equal to the Fair Market Value of Common Stock during the
30 days preceding such Outside Director's Service Ending Date multiplied by the
number of Performance Shares then held by such Outside Director.  An Outside
Director's Performance Bonus shall be paid to him or her in a lump sum.
Distribution with respect to an Outside Director shall not be made or commence
before the Outside Director ceases serving as a director of the Company. Upon
the death of an Outside Director while serving on the Board, such Outside
Director's Performance Bonus at the time of his or her death shall be paid to
the person who acquires such right by will or the laws of descent and
distribution or otherwise by reason of the death of the Outside Director.

     5.  Administration.  The Plan shall be administered by the Committee.
The Committee may, by a writing signed by a majority of its members, delegate
to any member or members of the Committee or to any employee or employees of
the Company the authority to perform any ministerial act in connection with the
administration of the Plan.

     The Committee shall have the authority to control and manage the operation
and administration of the Plan and the discretion to construe Plan provisions.
Subject to the provisions of the Plan, the Committee may from time to time
establish rules for the administration and interpretation of the Plan.  The
final determination of the Committee as to any disputed questions shall be
conclusive.

     6.  Adjustment on Changes in Capitalization.  In the event of any merger,
reorganization, consolidation, recapitalization, separation, spin-off,
liquidation, stock dividend, split-up, share combination or other change in the
corporate or capital structure of the Company affecting the Common Stock and
occurring during the term of an Outside Director's service as a director of the
Company, the number of Performance Shares previously granted to such Outside
Director pursuant to this Plan shall be equitably adjusted to prevent dilution
or enlargement of such Outside Director's rights hereunder and, if necessary,
provision shall be made for the substitution for the Performance Shares of new
performance shares related to the securities of a successor corporation or an
affiliate thereof, with appropriate adjustments as to the number and kind of
securities; provided that the total number of Performance Shares granted
hereunder shall always be a whole number.

     The existence of the Plan and the Performance Shares granted hereunder
shall not affect in any way the right or power of the Board or the shareholders
of the Company to make or authorize any adjustment, recapitalization,
reorganization or other change in the Company's capital structure or its
business, any merger or consolidation of the Company, any issue of debt or
equity securities ahead of or affecting Common Stock or the rights thereof, the
dissolution or liquidation of the Company or any sale, lease, exchange or other
disposition of all or any part of its assets or business or any other corporate
act or proceeding.

     7.  Miscellaneous.

        (a)  Unsecured Creditor Status.  This Plan, the Performance Shares to
be granted pursuant hereto, and the payment of Performance Bonuses as
contemplated herein are intended to constitute an "unfunded" compensation
arrangement for tax purposes and for purposes of Title I of ERISA.  The Plan
shall not be construed to create or require the Company to create a trust of
any kind to fund the amounts payable hereunder.  To the extent an Outside
Director or other person acquires a right to receive payments from the Company
in accordance with the Plan, such right shall be no greater than the right of
any general unsecured creditor of the Company.

        (b)  No Shareholder or Director Rights.  The Performance Shares are not
shares of Common Stock of the Company.  Neither this Plan nor the grant of any
Performance Shares shall confer on any Outside Director any right to continue
serving as a director of the Company.  Neither any Outside Director nor any
beneficiary of an Outside Director shall have any of the rights of a shareholder
of the Company with respect to the Performance Shares
including, without limitation, any right to receive dividends or dividend
equivalents declared or paid on the Common Stock.

        (c)  Nontransferability.  Performance Shares may not be sold,
transferred or otherwise disposed of and may not be pledged, hypothecated or
otherwise encumbered, except by will or the laws of descent and distribution.
The right of any Outside Director or any beneficiary to payments under the Plan
shall not be subject to alienation, assignment, garnishment, attachment,
execution or levy of any kind, and any attempt to cause such amounts to be so
subjected shall not be recognized by the Company.

        (d)  Amendment and Termination.  The Board reserves the right to amend
the Plan from time to time or terminate the Plan; provided, however, that no
such amendment or termination shall adversely affect the rights of any Outside
Director or beneficiary, without such person's prior written consent, with
respect to Performance Shares granted prior to such amendment or termination.
Performance Shares granted prior to an amendment or termination of the Plan
shall remain in full force and effect as if the Plan had not been amended or
terminated.

     IN WITNESS WHEREOF, the undersigned certifies that the Board adopted the
foregoing Plan on the Effective Date.

                                  /s/ Herbert D. Kelleher
                                  Herbert D. Kelleher, Chairman of the Board of
                                  Directors of Southwest Airlines Co.