1

                                                                     EXHIBIT 4.3





                          TRUST SUPPLEMENT NO. 1998-A
                            DATED AS OF MAY 1,  1998
                                       TO
                          PASS THROUGH TRUST AGREEMENT
                          DATED AS OF FEBRUARY 1, 1993


                             SOUTHWEST AIRLINES CO.
                                      AND
                      WILMINGTON TRUST COMPANY, AS TRUSTEE

                                  $95,531,435
   2

                                TRUST SUPPLEMENT


         This Trust Supplement No. 1998-A, dated as of May 1, 1998 (the "Trust
Supplement") between Southwest Airlines Co., a Texas corporation (the
"Company") and Wilmington Trust Company, a Delaware banking corporation (the
"Trustee"), to the Pass Through Trust Agreement dated as of February 1, 1993,
between the Company and the Trustee (the "Basic Agreement"),

                                  WITNESSETH:

         WHEREAS, the Company and the Trustee have heretofore executed and
delivered the Basic Agreement, unlimited as to the aggregate principal amount
of Certificates (unless specified herein capitalized terms used herein without
definition having the respective meanings specified heretofore in the Basic
Agreement) which may be issued thereunder;

         WHEREAS, each of four Owner Trustees, each acting on behalf of an
Owner Participant, has agreed to issue, on a non-recourse basis, Equipment
Notes, among other things, to finance the outstanding debt portion of the
purchase price of the aircraft heretofore purchased by such Owner Trustee and
leased to the Company pursuant to the related Lease;

         WHEREAS, pursuant to the terms and conditions of the Basic Agreement
as supplemented by this Trust Supplement (the "Agreement"), the Trustee shall
purchase such Equipment Notes issued by such Owner Trustees of the same tenor
as the Certificates issued hereunder and shall hold such Equipment Notes in
trust for the benefit of the Certificateholders;

         WHEREAS, the Trustee hereby declares the creation of this Trust (the
"1998-A Trust") for the benefit of the Certificateholders, and the initial
Certificateholders as the grantors of the 1998-A Trust, by their respective
acceptances of the Certificates, join in the creation of this 1998-A Trust with
the Trustee;

         WHEREAS, all of the conditions and requirements necessary to make this
Trust Supplement, when duly executed and delivered, a valid, binding and legal
instrument in accordance with its terms and for the purposes herein expressed,
have been done, performed and fulfilled, and the execution and delivery of this
Trust Supplement in the form and with the terms hereof have been in all
respects duly authorized;

         WHEREAS, this Trust Supplement is subject to the provisions of the
Trust Indenture Act and shall, to the extent applicable, be governed by such
provisions;

         NOW, THEREFORE, in consideration of the premises herein, it is agreed
between the Company and the Trustee as follows:



                          TRUST SUPPLEMENT NO. 1998-A
                                      -1-
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                                   ARTICLE I
                                THE CERTIFICATES

         Section 1.01     The Certificates.  Pursuant to Section 2.01 of the
Basic Agreement, there is hereby created a series of Certificates to be issued
under the Agreement to be distinguished and known as "Pass Through
Certificates, Series 1998-A" (hereinafter defined as the "Series 1998-A
Certificates").  Each Certificate represents a Fractional Undivided Interest in
the 1998-A Trust created hereby.  The terms and conditions applicable to the
Series 1998-A Certificates are as follows:

                 1.       The aggregate principal amount of the Series 1998-A
Certificates that shall be authenticated under the Agreement (except for Series
1998-A Certificates authenticated and delivered pursuant to Section 3.03, 3.04
or 3.05 of the Basic Agreement) upon their initial issuance is $95,531,435.

                 2.       The Cut-off Date is June 15, 1998.

                 3.       The Regular Distribution Dates with respect to any
payment of Scheduled Payments are January 2 and July 2 in each year, commencing
July 2, 1998, until payment of all of the Scheduled Payments to be made under
the Equipment Notes have been made.

                 4.       The Scheduled Payments shall be as set forth in
Exhibit C hereto.

                 5.       The Special Distribution Dates are as follows:  (i)
in the case of an early redemption of Equipment Note arising out of an Event of
Loss, a refinancing of the Equipment Notes or a purchase or early redemption by
the related Owner Participant or Owner Trustee of such Equipment Notes, an
early redemption of Equipment Notes arising out of a voluntary termination of
the related Lease pursuant to Section 9.1 thereof, or exercise by Lessee of a
purchase option, the date of the receipt of the applicable redemption or
purchase price therefor, which shall be a Business Day, and (ii) otherwise, the
earliest Business Day of a month for which it is practicable for the Trustee to
give notice pursuant to Section 4.02(c) of the Basic Agreement 20 days prior
thereto.

                 6.       The Series 1998-A Certificates shall be in the form
attached hereto as Exhibit A.  The Series 1998-A Certificates shall be
Book-Entry Certificates and shall be subject to the conditions set forth in the
Letter of Representations between the Company and the Clearing Agency attached
hereto as Exhibit B.

                 7.       The proceeds of the Series 1998-A Certificates shall
be used to purchase the Equipment Notes in the principal amounts specified
below:



                    Equipment Note            Principal Amount     Maturity
                    --------------            ----------------     --------
                                                             
                 Series SWA 1998 N620SW        $23,882,858.75      July 2, 2019
                 Series SWA 1998 N621SW        $23,882,858.75      July 2, 2019
                 Series SWA 1998 N622SW        $23,882,858.75      July 2, 2019
                 Series SWA 1998 N623SW        $23,882,858.75      July 2, 2019






                          TRUST SUPPLEMENT NO. 1998-A
                                      -2-
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         8.      Each of four Owner Trustees, each acting on behalf of an Owner
Participant, will issue on a non- recourse basis the Equipment Notes, the
proceeds of which shall be used to finance the debt portion of the purchase
price of the following Aircraft:



                                        Registration        Manufacturer's
                     Aircraft              Number           Serial Number
                     --------           -------------       -------------
                                                      
                 1 Boeing 737-3H4          N620SW               28036
                 1 Boeing 737-3H4          N621SW               28037
                 1 Boeing 737-3H4          N622SW               27932
                 1 Boeing 737-3H4          N623SW               27933


                 9.       The related Note Documents are as follows (with the
trust relating to each Note Document being indicated in parentheses for
purposes of identification):

                 (a)      Each of the following Indentures:

                          Trust Indenture and Security Agreement (Southwest
                          Airlines 1998 Trust N620SW) dated as of June 1, 1996,
                          as supplemented;

                          Trust Indenture and Security Agreement (Southwest
                          Airlines 1998 Trust N621SW) dated as of  June 1,
                          1996, as supplemented;

                          Trust Indenture and Security Agreement (Southwest
                          Airlines 1998 Trust N622SW) dated as of June 1, 1996,
                          as supplemented;

                          Trust Indenture and Security Agreement (Southwest
                          Airlines 1998 Trust N623SW) dated as of June 1, 1996,
                          as supplemented;

                 (b)      Each of the following Leases:

                          Sale and Lease Agreement (Southwest Airlines 1998
                          Trust N620W), dated as of June 1, 1996, as
                          supplemented;

                          Sale and Lease Agreement (Southwest Airlines 1998
                          Trust N621SW), dated as of June 1, 1996, as
                          supplemented;

                          Sale and Lease Agreement (Southwest Airlines 1998
                          Trust N622SW), dated as of June 1, 1996, as
                          supplemented;

                          Sale and Lease Agreement (Southwest Airlines 1998
                          Trust N623SW), dated as of June 1, 1996, as
                          supplemented;

                 (c)      Each of the following Participation Agreements:





                          TRUST SUPPLEMENT NO. 1998-A
                                      -3-
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                          Participation Agreement (Southwest Airlines 1998
                          Trust N620SW), dated as of June 1, 1996;

                          Participation Agreement (Southwest Airlines 1998
                          Trust N621SW), dated as of June 1, 1996;

                          Participation Agreement (Southwest Airlines 1998
                          Trust N622SW), dated as of June 1, 1996;

                          Participation Agreement (Southwest Airlines 1998
                          Trust N623SW), dated as of June 1, 1996;

                 (d)      Each of the following Trust Agreements:

                          Trust Agreement (Southwest Airlines 1998 Trust
                          N620SW) dated as of June 1, 1996, as supplemented;

                          Trust Agreement (Southwest Airlines 1998 Trust
                          N621SW) dated as of June 1, 1996, as supplemented;

                          Trust Agreement (Southwest Airlines 1998 Trust
                          N622SW) dated as of June 1, 1996, as supplemented;

                          Trust Agreement (Southwest Airlines 1998 Trust
                          N623SW) dated as of June 1, 1996, as supplemented;

                                   ARTICLE II
                                  THE TRUSTEE

         Section 2.01.    The Trustee.  The Trustee shall not be responsible in
any manner whatsoever for or in respect of the validity or sufficiency of this
Trust Supplement or the due execution hereof by the Company, or for or in
respect of the recitals and statements contained herein, all of which recitals
and statements are made solely by the Company.

         Except as herein otherwise provided, no duties, responsibilities or
liabilities are assumed, or shall be construed to be assumed by the Trustee by
reason of this Trust Supplement other than as set forth in the Basic Agreement,
and this Trust Supplement is executed and accepted on behalf of the Trustee,
subject to all the terms and conditions set forth in the Basic Agreement, upon
the effectiveness thereof, as fully to all intents as if the same were herein
set forth at length.

                                  ARTICLE III
                            MISCELLANEOUS PROVISIONS

         Section 3.01.    Basic Agreement Ratified.  Except and so far as
herein expressly provided, all of the provisions, terms and conditions of the
Basic Agreement are in all respects ratified and





                          TRUST SUPPLEMENT NO. 1998-A
                                      -4-
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confirmed; and the Basic Agreement and this Trust Supplement shall be taken,
read and construed as one and the same instrument.

         Section 3.02.    GOVERNING LAW.  THIS TRUST SUPPLEMENT AND THE SERIES
1998-A CERTIFICATES SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE
LAWS OF THE STATE OF DELAWARE.

         Section 3.03.    Execution in Counterparts.  This Trust Supplement may
be executed in any number of counterparts, each of which shall be an original,
but such counterparts shall together constitute but one instrument.





                          TRUST SUPPLEMENT NO. 1998-A
                                      -5-
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         IN WITNESS WHEREOF, the Company and the Trustee have caused this Trust
Supplement to be duly executed by their respective officers thereto duly
authorized, as of the day and year first above written.

                                   SOUTHWEST AIRLINES CO.



                                   By                                    
                                       ------------------------------------    
                                       Treasurer

                                   WILMINGTON TRUST COMPANY, not in
                                       its individual capacity, but solely
                                       as Trustee



                                   By                                    
                                       ------------------------------------    
                                   Title:






                          TRUST SUPPLEMENT NO. 1998-A
                                      -6-
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                                   EXHIBIT A

CUSIP NO.  84474 WAA 8       [FORM OF CERTIFICATE]

         **Unless this certificate is presented by an authorized representative
of The Depository Trust Company, a New York Corporation ("DTC"), to Issuer or
its agent for registration of transfer, exchange or payment, and any
certificate issued is registered in the name of Cede & Co. or in such other
name as is requested by an authorized representative of DTC (and any payment is
made to Cede & Co. or to such other entity as is requested by an authorized
representative of DTC), ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR
OTHERWISE BY OR TO ANY PERSON IS WRONGFUL inasmuch as the registered owner
hereof, Cede & Co., has an interest herein.

                  SOUTHWEST AIRLINES 1998-A PASS THROUGH TRUST

                                  Pass Through
                           Certificate, Series 1998-A

                     Final Distribution Date: July 2, 2019

                 evidencing a fractional undivided interest in a trust, the
                 property of which includes certain Equipment Notes each
                 secured by an Aircraft leased to Southwest Airlines Co.

Certificate
No. ______            $ ________Fractional Undivided Interest representing
                      _________% of the Trust per $1,000 face amount.

         THIS CERTIFIES THAT ___________________________________________, for
value received, is the registered owner of a $__________________________
(_____________ dollars) Fractional Undivided Interest in the Southwest Airlines
1998-A Pass Through Trust (the "Trust") created by Wilmington Trust Company, as
trustee (the "Trustee"), pursuant to a Pass Through Trust Agreement dated as of
February 1, 1993 (the "Basic Agreement"), as supplemented by Trust Supplement
No. 1998-A thereto dated as of May 1, 1998 (collectively, the "Agreement"),
between the Trustee and Southwest Airlines Co., a corporation incorporated
under Texas law (the "Company"), a summary of certain of the pertinent
provisions of which is set forth below.  To the extent not otherwise defined
herein, the capitalized terms used herein have the meanings assigned to them in
the Agreement.  This Certificate is one of the duly authorized Certificates
designated as "Pass Through Certificates, Series 1998-A" (herein called the
"Certificates").  This Certificate is issued under and is subject to the terms,
provisions, and conditions of the Agreement, to which Agreement the
Certificateholder of this Certificate by virtue of the acceptance hereof
assents and by which such Certificateholder is bound.  The property of the
Trust includes certain Equipment Notes or, pending the acquisition thereof,
certain cash or Specified Investments (the "Trust Property").  Each issue of
the Equipment Notes, when issued, will be secured by a security interest in an
aircraft leased to the Company.

         The Certificates represent Fractional Undivided Interests in the Trust
and the Trust Property, and have no rights, benefits or interest in respect of
any other separate trust established pursuant to the terms of the Basic
Agreement for any other series of certificates issued pursuant thereto.  _

         **      This legend to appear on Book-Entry Certificates to be
                 deposited with The Depository Trust Company.  One Certificate
                 may be issued in a denomination of less than $1,000 which
                 shall not have this legend.





                          TRUST SUPPLEMENT NO. 1998-A
                                      A-1
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         Subject to and in accordance with the terms of the Agreement, from
funds then available to the Trustee, there will be distributed on January 2 and
July 2 in each year, commencing July 2, 1998 (a "Regular Distribution Date") to
the Person in whose name this Certificate is registered at the close of
business on the 15th day preceding the Regular Distribution Date, an amount in
respect of the Scheduled Payments on the Equipment Notes due on such Regular
Distribution Date, the receipt of which has been confirmed by the Trustee,
equal to the product of the percentage interest in the Trust evidenced by this
Certificate and an amount equal to the sum of such Scheduled Payments.  Subject
to and in accordance with the terms of the Agreement, in the event that Special
Payments are received by the Trustee, from funds then available to the Trustee,
there shall be distributed on the applicable Special Distribution Date, to the
Person in whose name this Certificate is registered at the close of business on
the 15th day preceding the Special Distribution Date, an amount in respect of
such Special Payments, the receipt of which has been confirmed by the Trustee,
equal to the product of the percentage interest in the Trust evidenced by this
Certificate and an amount equal to the sum of such Special Payments so
received.  If a Regular Distribution Date or Special Distribution Date is not a
Business Day, distribution shall be made on the immediately following Business
Day with the same force and effect as if made on such Regular Distribution Date
or Special Distribution Date and no interest shall accrue during the
intervening period.  The Trustee shall mail notice of each Special Payment and
the Special Distribution Date therefor to the Certificateholder of this
Certificate.

         Distributions on this Certificate will be made by the Trustee in
immediately available funds to the Person entitled thereto, without the
presentation or surrender of this Certificate or the making of any notation
hereon.  Except as otherwise provided in the Agreement and notwithstanding the
above, the final distribution on this Certificate will be made after notice
mailed by the Trustee of the pendency of such distribution and only upon
presentation and surrender of this Certificate at the office or agency of the
Trustee specified in such notice.

         The Certificates do not represent a direct obligation of, or an
obligation guaranteed by, or an interest in, the Company or the Trustee or any
affiliate thereof.  The Certificates are limited in right or payment, all as
more specifically set forth herein and in the Agreement.  All payments or
distributions made to Certificateholders under the Agreement shall be made only
from the Trust Property and only to the extent that the Trustee shall have
sufficient income or proceeds from the Trust Property to make such payments in
accordance with the terms of the Agreement.  Each Certificateholder of this
Certificate, by its acceptance hereof, agrees that it will look solely to the
income and proceeds from the Trust Property to the extent available for
distribution to such Certificateholder as provided in the Agreement.  This
Certificate does not purport to summarize the Agreement and reference is made
to the Agreement for information with respect to the interests, rights,
benefits, obligations, proceeds, and duties, evidenced hereby.  A copy of the
Agreement may be examined during normal business hours at the principal office
of the Trustee, and at such other places, if any, designated by the Trustee, by
any Certificateholder upon request.

         The Agreement permits, with certain exceptions therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Certificateholders under the Agreement at any
time by the Company and the Trustee with the consent





                          TRUST SUPPLEMENT NO. 1998-A
                                      A-2
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of the Certificateholders holding Certificates evidencing Fractional Undivided
Interests aggregating not less than a majority in interest in the Trust.  Any
such consent by the Certificateholder of this Certificate shall be conclusive
and binding on such Certificateholder and upon all future Certificateholders of
this Certificate and of any Certificate issued upon the transfer hereof or in
exchange hereof or in lieu hereof whether or not notation of such consent is
made upon this Certificate.  The Agreement also permits the amendment thereof,
in certain limited circumstances, without the consent of the Certificateholders
of any of the Certificates.

         As provided in the Agreement and subject to certain limitations
therein set forth, the transfer of this Certificate is registrable in the
Register upon surrender of this Certificate for registration of transfer at the
offices or agencies maintained by the Trustee in its capacity as Registrar, or
by any successor Registrar, duly endorsed or accompanied by a written
instrument of transfer in form satisfactory to the Trustee and the Registrar
duly executed by the Certificateholder hereof or such Certificateholder's
attorney duly authorized in writing, and thereupon one or more new Certificates
of authorized denominations evidencing the same aggregate Fractional Undivided
Interest in the Trust will be issued to the designated transferee or
transferees.

         The Certificates are issuable only as registered Certificates without
coupons in minimum denominations of $1,000 or integral multiples thereof except
that one Certificate may be in a denomination of less than $1,000.  As provided
in the Agreement and subject to certain limitations therein set forth, the
Certificates are exchangeable for new Certificates of authorized denominations
evidencing the same aggregate Fractional Undivided Interest in the Trust, as
requested by the Certificateholder surrendering the same.

         No service charge will be made for any such registration of transfer
or exchange, but the Trustee shall require payment of a sum sufficient to cover
any tax or governmental charge payable in connection therewith.

         The Trustee, the Registrar, and any agent of the Trustee or the
Registrar may treat the Person in whose name this Certificate is registered as
the owner hereof for all purposes, and none of the Trustee, the Registrar, or
any such agent shall be affected by any notice to the contrary.

         The obligations and responsibilities created by the Agreement and the
Trust created thereby shall terminate upon the distribution to
Certificateholders of all amounts required to be distributed to them pursuant
to the Agreement and the disposition of all property held as part of the Trust
Property.

         THE AGREEMENT AND THIS CERTIFICATE SHALL BE GOVERNED BY AND CONSTRUED
IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE.

         Unless the certificate of authentication hereon has been executed by
the Trustee, by manual signature, this Certificate shall not be entitled to any
benefit under the Agreement or be valid for any purpose.





                          TRUST SUPPLEMENT NO. 1998-A
                                      A-3
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         IN WITNESS WHEREOF, the Trustee has caused this Certificate to be duly
executed.

                                     SOUTHWEST AIRLINES 1998-A
                                     PASS THROUGH TRUST

                                     By: WILMINGTON TRUST COMPANY, not
                                         in its individual capacity but
                                         solely as Trustee


                                     By:                                       
                                         --------------------------------------
                                     Title:                                    
                                              ---------------------------------


Dated:   May 29, 1998





                          TRUST SUPPLEMENT NO. 1998-A
                                      A-4
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         [FORM OF THE TRUSTEE'S CERTIFICATE OF AUTHENTICATION]


                    This is one of the Certificates referred
                     to in the within-mentioned Agreement.


                                   WILMINGTON TRUST COMPANY, not in its
                                       individual capacity, but solely as
                                       Trustee



                                   By:                                      
                                      --------------------------------------
                                            Authorized Officer






                          TRUST SUPPLEMENT NO. 1998-A
                                      A-5
   13
                                   EXHIBIT B


                          TRUST SUPPLEMENT NO. 1998-A
                            Dated as of May 1, 1998

                        [DTC LETTER OF REPRESENTATIONS]





                          TRUST SUPPLEMENT NO. 1998-A
                                      B-1
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                                   EXHIBIT C


                          TRUST SUPPLEMENT NO. 1998-A
                            Dated as of May 1, 1998


                               Scheduled Payments



                                                Percentage of Original
Principal Payment Date                             Principal Amount   
- ----------------------                          ----------------------
                                             
                                                     -----------------
                                                         100.000000000
                                                     =================
                                        
                                                




                          TRUST SUPPLEMENT NO. 1998-A
                                      C-1