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                                                                   EXHIBIT 10.13

                             SOUTHWEST AIRLINES CO.

                      1996 NON-QUALIFIED STOCK OPTION PLAN

         SOUTHWEST AIRLINES CO., a Texas corporation (the "Company"), hereby
formulates and adopts the following 1996 Non-Qualified Stock Option Plan (the
"Plan") for employees and directors of the Company and its subsidiaries.

         1. Purpose. The purpose of this Plan is to secure for the Company the
benefits of the additional incentive inherent in the ownership of its Common
Stock by selected key employees and directors of the Company and its
subsidiaries who are important to the success and the growth of the Company and
its subsidiaries, and to help the Company and its subsidiaries secure and retain
the services of such key employees and directors.

         2. Stock Option Committee. Subject to the provisions of paragraph 4,
this Plan shall be administered by a Stock Option Committee (the "Committee") of
the Board of Directors (the "Board") of the Company, to be appointed by at least
a majority of the whole Board of Directors. All members of the Committee shall
be "disinterested" within the meaning of Rule 16b-3 under the Securities
Exchange Act of 1934, as such Rule is in effect on the date of adoption of this
Plan by the Board. The Committee shall select one of its members as Chairman and
shall adopt such rules and regulations as it shall deem appropriate concerning
the holding of its meetings and the transaction of its business. A majority of
the whole Committee shall constitute a quorum, and the act of a majority of the
members of the Committee present at a meeting at which a quorum is present shall
be the act of the Committee. Any member of the Committee may be removed at any
time either with or without cause by resolution adopted by the Board of
Directors of the Company; and any vacancy on the Committee may at any time be
filled by resolution adopted by the Board of Directors.

         3. Grant of Options. The Committee shall have the authority and
responsibility, within the limitations of this Plan, to determine the key
employees to whom options are to be granted, the number of shares that may be
purchased under each option and the option price.

         In determining the key employees to whom options shall be granted and
the number of shares to be covered by each such option, the Committee shall take
into consideration the employee's present and potential contribution to the
success of the Company and its subsidiaries and such other factors as the
Committee may deem proper and relevant. During any calendar year period during
the term of this Plan, options will not be granted to any individual in excess
of 50,000 shares, as adjusted from time to time pursuant to paragraph 13.

         Options may not be granted under this Plan if shares are available for
granting under the 1991 Non-Qualified Stock Option Plan.

         4. Persons Eligible.

         (a) Options may be granted under this Plan to any key employee or
prospective key employee (conditioned and effective upon his becoming an
employee) of the Company or its subsidiaries. Employees who are also officers or
directors of the Company or its subsidiaries shall not by reason of such offices
be ineligible to receive options under this Plan.


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         (b) Each individual who is not an employee of the Company or its
subsidiaries, who becomes a director of the Company ("Outside Director") after
adoption of this Plan and who has not previously been granted options under
this, or any other stock option plan of the Company, shall, on the date of his
or her election to the Board of Directors of the Company, be granted an option
to purchase 10,000 shares of the Common Stock at a price equal to 100% of the
fair market value of the Common Stock on such date. No Outside Director to whom
an option has been granted shall be eligible to receive additional options under
this Plan.

         An employee or director receiving any option under this Plan is
hereinafter referred to as an "Optionee." Any reference herein to the employment
of an Optionee with the Company shall include employment with the Company or any
of its subsidiaries. The fair market value of the Common Stock on any day shall
be the mean between the highest and lowest quoted selling prices of the Common
Stock on such day as reported by the primary national stock exchange on which
such stock is listed. If no sale shall have been made on that day, or if the
Common Stock is not listed on a national exchange at that time, fair market
value will be determined by the Committee.

         5. Stock Subject to Options. Subject to the provisions of paragraph 13,
the number of shares of the Company's Common Stock subject at any one time to
options, plus the number of such shares then outstanding pursuant to exercises
of options granted under this Plan, shall not exceed 575,000. If, and to the
extent the options granted under this Plan terminate or expire without having
been exercised, new options may be granted with respect to the shares covered by
such terminated or expired options; provided that the granting and terms of such
new options shall in all respects comply with the provisions of this Plan.

         Shares sold or distributed upon the exercise of any option granted
under this Plan may be shares of the Company's authorized and unissued Common
Stock, shares of the Company's issued Common Stock held in the Company's
treasury, or both.

         There shall be reserved at all times for sale or distribution under
this Plan a number of shares of Common Stock (either authorized and unissued
shares or shares held in the Company's treasury, or both) equal to the maximum
number of shares which may be purchased or distributed upon the exercise of
options granted or that may be granted under this Plan.

         6. Option Price. The option price of each share of Common Stock
purchasable under any option granted under this Plan shall be not less than the
fair market value thereof at the time the option is granted and shall be set
forth in the option agreement.

         7. Expiration and Termination of the Plan. Options may be granted under
this Plan at any time and from time to time, prior to December 31, 2005, on
which date this Plan will expire, except as to options then outstanding under
this Plan. Such options shall remain in effect until they have been exercised or
have expired. This Plan may be terminated or modified at any time prior to
December 31, 2005, by the Board of Directors except with respect to any options
then outstanding under this Plan; provided that any (a) increase in the maximum
number of shares subject to options, as specified in paragraph 5, (b) decrease
in the minimum option price specified in paragraph 6 or (c) change in the number
of and terms of options to be awarded to Outside Directors as specified in
paragraphs 4(b), 8 and 13 shall be subject to approval by the Company's
shareholders, unless made pursuant to the provisions of paragraph 13.

         No modification, extension, renewal or other change in any option
granted under this Plan shall be made after the grant of such option unless the
same is consistent with the provisions of this Plan.


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         8. Exercisability and Duration of Options.

         (a) Exercisability. Options granted under this Plan to employees shall
become exercisable after the lapse of such period or periods of time or the
occurrence of such event or events as the Committee, in its discretion, may
provide upon the granting thereof. Any option granted under this Plan to an
Outside Director shall become exercisable as follows (or after the lapse of such
additional period or periods of time or the occurrence of such event or events
as the Committee, in its discretion, may provide upon the granting thereof):

<Table>
<Caption>
                  Time Elapsed since Grant           Options First Exercisable
                  ------------------------           -------------------------
<S>                                                  <C>
                           One Year                            1,000
                           Two Years                           1,500
                           Three Years                         2,000
                           Four Years                          2,500
                           Five Years                          3,000
</Table>

         After the expiration of five years following the date on which such
grant is made, such options may be exercised as to all of the shares covered
thereby.

         (b) Duration. The unexercised portion of any option granted under this
Plan shall automatically and without notice terminate and become null and void
at the time of the earliest to occur of the following:

                  (1) The expiration of 10 years from the date on which such
option was granted;

                  (2) The expiration of three months from the date of
termination of the Optionee's employment with the Company or any subsidiary (or
in the case of an Outside Director, three months from the date such Outside
Director ceases to serve as a member of the Board of Directors for any reason
other than death); provided that if the Optionee shall die during such 3-month
period the provisions of subparagraph (3) below shall apply;

                  (3) The expiration of 6 months following the issuance of
letters testamentary or letters of administration to the executor or
administrator of a deceased Optionee, if the Optionee's death occurs either
during his employment with the Company (or service as an Outside Director, as
the case may be) or during the 3-month period following the date of termination
of such employment (or service as an Outside Director, as the case may be), but
not later than 1 year after the Optionee's death;

                  (4) In the case of employee Optionees, the termination of the
Optionee's employment with the Company for cause, including breach by the
Optionee of an employment agreement with the Company or any of its subsidiaries
or the Optionee's commission of a felony or misdemeanor (whether or not
prosecuted) against the Company or any of its subsidiaries;

                  (5) In the case of employee Optionees, the expiration of such
period of time or the occurrence of such event as the Committee in its
discretion may provide upon the granting thereof.


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         9. Exercise of Options.

         (a) Procedure. The options granted hereunder shall be exercised by the
Optionee (or by the person who acquires such options by will or the laws of
descent and distribution or otherwise by reason of the death of the Optionee) as
to all or part of the shares covered by the option, by giving written notice
(the "Notice") of the exercise thereof to the Company. From time to time the
Committee may establish procedures relating and effecting such exercises. No
fractional shares shall be issued as a result of exercising an option.

         (b) Payment. In the Notice, the Optionee shall elect whether he or she
is to pay for his or her shares in cash or in Common Stock of the Company, or
both. If payment is to be made in cash, the Optionee shall deliver to the
Company a cashier's check or electronic funds transfer in the amount of the
exercise price on or before the exercise date. If payment is to be made in
Common Stock, it shall be valued at its fair market value on the date of such
notice, as determined pursuant to paragraph 6 hereof and the Notice shall be
accompanied by a certificate for at least the number of shares of Common Stock
to be used as payment.

         (c) Irrevocable Election. The giving of such written notice to the
Company shall constitute an irrevocable election to purchase the number of
shares specified in the Notice on the date specified in the Notice.

         (d) Withholding Taxes. To the extent that the exercise of any Option
granted pursuant to this Plan or the disposition of shares of Common Stock
acquired by exercise of an Option results in compensation income to the Optionee
for federal or state income tax purposes, the Optionee shall deliver to the
Company at the time of such exercise or disposition such amount of money as the
Company may require to meet its obligation under applicable tax laws or
regulations, and, if the Optionee fails to do so, the Company is authorized to
(a) withhold delivery of certificates upon exercise and (b) withhold from
remuneration then or thereafter payable to Optionee any tax required to be
withheld by reason of such resulting compensation income.

         (e) Delivery of Shares. The Company shall cause certificates for shares
to be delivered to the Optionee (or the person exercising the Optionee's options
in the event of the death as soon as practicable after the exercise date.

         10. Nontransferability of Options. No option granted under this Plan or
any right evidenced thereby shall be transferable by the Optionee other than by
will or the laws of descent and distribution. During the lifetime of an
Optionee, only the Optionee (or his or her guardian or legal representative) may
exercise his options.

         In the event of the Optionee's death during his or her employment with
the Company, or during the 30-day period following the date of termination of
such employment, his options shall thereafter be exercisable, as provided in
paragraph 8(b), by the person who acquires such options by will or the laws of
descent and distribution or otherwise by reason of the death of the Optionee.

         11. Rights of Optionee. Neither the Optionee nor his or her executors,
administrators, or legal representatives shall have any of the rights of a
shareholder of the Company with respect to the shares subject to an option
granted under this Plan until certificates for such shares shall have been
issued upon the exercise of such option.



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         12. Right to Terminate Employment. Nothing in this Plan or in any
option granted under this Plan shall confer upon any Optionee the right to
continue in the employment of the Company or affect the right of the Company or
any of its subsidiaries to terminate the Optionee's employment at any time,
subject, however, to the provisions of any agreement of employment between the
Company or any of its subsidiaries and the Optionee.

         13. Adjustment Upon Changes in Capitalization, Etc.

         (a) The existence of the Plan and the options 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.

         (b) The shares with respect to which options may be granted are shares
of Common Stock as presently constituted, but if, and whenever, prior to the
expiration of an option theretofore granted, the Company shall effect a
subdivision or consolidation of shares of Common Stock or the payment of a stock
dividend on Common Stock without receipt of consideration by the Company, the
number of shares of Common Stock with respect to which such option may
thereafter be exercised (i) in the event of an increase in the number of
outstanding shares shall be proportionately increased, and the purchase price
per share shall be proportionately reduced, and (ii) in the event of a reduction
in the number of outstanding shares shall be proportionately reduced, and the
purchase price per share shall be proportionately increased. In the event of any
such change in the outstanding Common Stock, the aggregate number of shares
available under the Plan may be appropriately adjusted by the Committee whose
determination shall be conclusive.

         (c) If the Company recapitalizes or otherwise changes its capital
structure, thereafter upon any exercise of an option theretofore granted the
Optionee shall be entitled to purchase under such option, in lieu of the number
of shares of Common Stock as to which such option shall then be exercisable, the
number and class of shares of stock and securities to which the Optionee would
have been entitled pursuant to the terms of the recapitalization if, immediately
prior to such recapitalization, the Optionee had been the holder of record of
the number of shares of Common Stock as to which such option is then
exercisable. If the Company shall not be the surviving entity in any merger or
consolidation (or survives only as a subsidiary of an entity other than a
previously wholly-owned subsidiary of the Company) or if the Company is to be
dissolved or liquidated, then unless a surviving corporation assumes or
substitutes new options for Options then outstanding hereunder (i) the time at
which such Options may be exercised shall be accelerated and such Options shall
become exercisable in full on or before a date fixed by the Company prior to the
effective date of such merger or consolidation or such dissolution or
liquidation, and (ii) upon such effective date Options shall expire.

         (d) Except as hereinbefore expressly provided, the issuance by the
Company of shares of stock of any class or securities convertible into shares of
stock of any class, property, labor or services, upon direct sale, upon the
exercise of rights or warrants to subscribe therefor, or upon conversion of
shares or obligations of the Company convertible into such shares or other
securities, and in any case whether or not for fair value, shall not affect, and
no adjustment by reason thereof shall be made with respect to, the number of
shares of Common Stock subject to options theretofore granted or the purchase
price per share.



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         14. Purchase for Investment and Legality. The Optionee, by the
acceptance of any option granted under this Plan, shall represent and warrant to
the Company that the purchase or receipt of shares of Common Stock upon the
exercise thereof shall be for investment and not with a view to distribution,
provided that such representation and warranty shall be inoperative if, in the
opinion of counsel to the Company, a proposed sale or distribution of such
shares is pursuant to an applicable effective registration statement under the
Securities Act of 1933 or is, without such representation and warranty, exempt
from registration under such Act.

         The obligation of the Company to issue shares upon the exercise of an
option shall also be subject as conditions precedent to compliance with
applicable provisions of the Securities Act of 1933, the Securities Exchange Act
of 1934, state securities laws, rules and regulations under any of the foregoing
and applicable requirements of any securities exchange upon which the Company's
securities shall be listed.

         The Company may endorse an appropriate legend referring to the
foregoing restrictions upon the certificate or certificates representing any
shares issued or transferred to the Optionee upon the exercise of any option
granted under this Plan.

         15. Effective Date of Plan. This Plan shall become effective upon its
adoption by the Board of Directors of the Company, subject, however, to its
approval by the Company's shareholders after the date of such adoption.



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