<PAGE>   1
                                                                    EXHIBIT 10.1

                          Supplemental Agreement No. 8

                                       to

                           Purchase Agreement No. 1810

                                     between

                               The Boeing Company

                                       and

                             SOUTHWEST AIRLINES CO.

                    Relating to Boeing Model 737-7H4 Aircraft


         THIS SUPPLEMENTAL AGREEMENT, entered into as of March 20, 1999, by and
between THE BOEING COMPANY, a Delaware corporation with its principal offices in
Seattle, Washington, (Boeing) and SOUTHWEST AIRLINES CO., a Texas corporation
with its principal offices in City of Dallas, State of Texas (Buyer);

         WHEREAS, the parties hereto entered into Purchase Agreement No. 1810
dated January 19, 1994, relating to Boeing Model 737-7H4 aircraft (the
Agreement) and;

         WHEREAS, Buyer has agreed to exercise the option to purchase six (6)
additional Option Aircraft and to accelerate delivery of those Option Aircraft
from July 2006 (2) and October 2006 four (4) to June 2000 three (3), July 2000
one (1) and August 2000 two (2);

         NOW THEREFORE, in consideration of the mutual covenants herein
contained, the parties agree to amend the Agreement as follows:

--------------------------------------------------------------------------------

***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.





P.A. No. 1810                       SA-8-1
K/SWA

<PAGE>   2

1. The Table of Contents of the Agreement is deleted in its entirety and a new
Table of Contents is attached hereto and incorporated into the Agreement by this
reference.

2. Article 1, entitled "Subject Matter of Sale," paragraph 1.1 entitled "The
Aircraft" is deleted in its entirety and replaced by a new paragraph 1.1 revised
to reflect one hundred thirty-six (136) Aircraft. Such new page 1-1 is attached
hereto and incorporated into the Agreement by this reference.

3. Article 2, entitled "Delivery, Title and Risk of Loss," paragraph 2.1,
entitled "Time of Delivery," is deleted in its entirety and replaced by a new
paragraph 2.1 revised to add three (3) Block "L" Aircraft for delivery in June
2000, to add one (1) Block "L" Aircraft for delivery in July 2000 and to add two
(2) Block "L" Aircraft for delivery in August 2000. Such new pages 2-1, 2-2 and
2-3 are attached hereto and incorporated into the Agreement by this reference.

4. Article 3, entitled "Price of Aircraft", paragraph 3.4 entitled "Advance
Payment Base Price," subparagraph 3.4.1 entitled "Advance Payment Base Price" is
revised by adding Advance Payment Base Prices for the Block "L" June 2000, July
2000 and August 2000 Aircraft. Such new pages 3-1, 3-2, 3-3 and 3-4 are attached
hereto and incorporated into the Agreement by this reference.

5. Letter Agreement No. 6-1162-RLL-933R6 entitled "Option Aircraft" is deleted
in its entirety and replaced with Letter Agreement No. 6-1162-RLL-933R7 attached
hereto and incorporated herein by this reference. The third paragraph is revised
to refer to fifty-two (52) Rollover Option Aircraft. Article 2 entitled
"Delivery of Rollover Option Aircraft," paragraph 2.1 is revised to change the
quantity of Rollover Option Aircraft from eighteen (18) to twelve (12) in the
year 2009; paragraph 2.2 and subparagraphs 2.2.1 and 2.2.2 are revised by
changing the quantity of Rollover Option Aircraft from fifty-eight (58) to
fifty-two (52).



P.A. No. 1810                       SA-8-2
K/SWA

<PAGE>   3

6. All references in the Letter Agreements associated with Purchase Agreement
No. 1810 shall be deemed to refer to the purchase by Buyer of one hundred
thirty-six (136) Model 737-7H4 Aircraft, sixty-two (62) Model 737-7H4 Option
Aircraft and fifty-two (52) Model 737-7H4 Rollover Option Aircraft, to the
extent such reference is not specifically addressed herein.

7. Concurrent with execution of this Supplemental Agreement, Buyer will pay to
Boeing ***. Such amount reflects the difference in advance payments due as a
result of the exercise of the Option to purchase six Aircraft and the deposits
due for six Rollover Option Aircraft converted to Option Aircraft.

The Agreement will be deemed to be supplemented to the extent herein provided
and as so supplemented will continue in full force and effect.

EXECUTED IN DUPLICATE as of the day and year first above written.

THE BOEING COMPANY                  SOUTHWEST AIRLINES CO.



By:    /s/ DAWN S. FOSTER           By:  /s/ LAURA WRIGHT
    ------------------------           ---------------------

Its:    ATTORNEY-IN-FACT            Its:    TREASURER
     -----------------------            --------------------



P.A. No. 1810                       SA-8-3
K/SWA

<PAGE>   4

                               PURCHASE AGREEMENT

                                     between

                               THE BOEING COMPANY

                                       and

                             SOUTHWEST AIRLINES CO.






                    Relating to Boeing Model 737-7H4 Aircraft

                         Purchase Agreement Number 1810













***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.


P.A. No. 1810                          i
K/SWA                                                                       SA-8

<PAGE>   5

                                TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                              Page            SA
                                                                            Number        Number
                                                                            ------        ------

ARTICLES
--------


<S>           <C>                                                           <C>           <C>
1.            Subject Matter of Sale..........................................1-1          SA-8

2.            Delivery, Title and Risk
              of Loss.........................................................2-1          SA-8

3.            Price of Aircraft...............................................3-1          SA-8

4.            Taxes...........................................................4-1

5.            Payment.........................................................5-1

6.            Excusable Delay.................................................6-1

7.            Changes to the Detail
              Specification...................................................7-1          SA-1

8.            Federal Aviation Requirements and
              Certificates and Export License.................................8-1

9.            Representatives, Inspection,
              Flights and Test Data...........................................9-1

10.           Assignment, Resale or Lease....................................10-1

11.           Termination for Certain Events.................................11-1

12.           Product Assurance; Disclaimer and
              Release; Exclusion of Liabilities;
              Customer Support; Indemnification
              and Insurance..................................................12-1

13.           Buyer Furnished Equipment and
              Spare Parts....................................................13-1

14.           Contractual Notices and Requests...............................14-1

15.           Miscellaneous..................................................15-1
</TABLE>


P.A. No. 1810                         ii
K/SWA                                                                       SA-8

<PAGE>   6

                                TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                           SA
                                                                       Number
                                                                       ------

EXHIBITS
--------


<S>           <C>                                                        <C>
A             Aircraft Configuration                                     SA-1

B             Product Assurance Document                                 SA-1

C             Customer Support Document

D             Price Adjustments Due to
              Economic Fluctuations - Aircraft

E             Buyer Furnished Equipment
              Provisions Document

F             Defined Terms Document



LETTER AGREEMENTS
-----------------


1810-1        Waiver of Aircraft Demonstration Flight
</TABLE>



P.A. No. 1810                         iii
K/SWA                                                                       SA-8

<PAGE>   7

                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                 SA
                                                                                             Number
                                                                                             ------
RESTRICTED LETTER AGREEMENTS
----------------------------


<S>                            <C>                                                          <C>
6-1162-RLL-932                 Promotional Support

6-1162-RLL-933R7               Option Aircraft                                               SA-8

6-1162-RLL-934R1               Disclosure of Confidential                                    SA-1
                               Information

6-1162-RLL-935R1               Performance Guarantees                                        SA-1

6-1162-RLL-936R4               Certain Contractual Matters                                   SA-4

6-1162-RLL-937                 Alternate Advance Payment Schedule

6-1162-RLL-938                 ***

6-1162-RLL-939R1               Certification Flight Test Aircraft                            SA-1

6-1162-RLL-940R1               Training Matters                                              SA-1

6-1162-RLL-941R1               Other Matters                                                 SA-1

6-1162-RLL-942                 Open Configuration Matters

6-1162-RLL-943R1               Substitution Rights                                           SA-6

6-1162-RLL-944                 Airframe Maintenance Material Cost
                               Protection Program

6-1162-RLL-945                 Comparison of 737-7H4 and 737-3H4
                               Block Fuel Burn

6-1162-RLL-1855R3              Additional Contractual Matters                                SA-4

6-1162-RLL-1856                ***                                                           SA-1

6-1162-RLL-1857                Service Ready Validation Program                              SA-1
                               Field Test

6-1162-RLL-1858R1              Escalation Matters                                            SA-4
</TABLE>



P.A. No. 1810                          iv
K/SWA                                                                       SA-8

<PAGE>   8

                             TABLE OF CONTENTS CON'T

<TABLE>
<CAPTION>
                                                                                                 SA
                                                                                             Number
                                                                                             ------
RESTRICTED LETTER AGREEMENTS
----------------------------


<S>                            <C>                                                          <C>
6-1162-RLL-2036                Amortization of Costs for
                               Customer Unique Changes                                       SA-1

6-1162-RLL-2037                Reconciliation of the Aircraft                                SA-1
                               Basic Price

6-1162-RLL-2073                Maintenance Training Matters                                  SA-1
</TABLE>


P.A. No. 1810                          v
K/SWA                                                                       SA-8

<PAGE>   9

                           PURCHASE AGREEMENT NO. 1810

                                   Relating to

                          BOEING MODEL 737-7H4 AIRCRAFT

                           --------------------------


         This Agreement is entered into as of January 19th 1994, by and between
The Boeing Company, a Delaware corporation, with its principal office in
Seattle, Washington (Boeing), and Southwest Airlines Co., a Texas corporation,
with its principal office in the City of Dallas, State of Texas (Buyer).


Accordingly, Boeing and Buyer agree as follows:




P.A. No. 1810                         1-1
K/SWA                                                                       SA-8

<PAGE>   10

ARTICLE 1. Subject Matter of Sale.

         1.1 The Aircraft. Subject to the terms and conditions of this
Agreement, Boeing will manufacture and deliver to Buyer and Buyer will purchase
and accept delivery from Boeing of one hundred thirty-six (136) Boeing Model
737-7H4 aircraft (the Aircraft) manufactured in accordance with Boeing Detail
Specification D6-38808-1, dated October 30, 1996, as described in Exhibit A, as
modified from time to time in accordance with this Agreement (Detail
Specification).

         1.2 Additional Goods and Services. In connection with the sale of the
Aircraft, Boeing will also provide to Buyer certain other things under this
Agreement, including data, documents, training and services, all as described in
this Agreement.

         1.3 Performance Guarantees. Any performance guarantees applicable to
the Aircraft will be expressly included in this Agreement. Where performance
guarantees are included in this Agreement other than within the Detail
Specification, such guarantees will be treated as being incorporated in the
Detail Specification by this reference.

         1.4 Defined Terms. For ease of use, certain terms are treated as
defined terms in this Agreement. Such terms are identified with a capital letter
and set forth and/or defined in Exhibit F.




P.A. No. 1810                         1-2
K/SWA

<PAGE>   11

ARTICLE 2. Delivery, Title and Risk of Loss.

         2.1 Time of Delivery. The Aircraft will be delivered to Buyer by
Boeing, assembled and ready for flight and Buyer will accept delivery of the
Aircraft, in accordance with the following schedule:

<TABLE>
<CAPTION>
             Month and Year
               of Delivery                           Quantity of Aircraft
             --------------                          --------------------
<S>          <C>                <C>                  <C>
                                Block A Aircraft
                                ----------------
             October 1997                                     Two (2)
             November 1997                                    Two (2)

                                Block B Aircraft
                                ----------------
             January 1998                                     Two (2)
             February 1998                                    Three (3)
             March 1998                                       Two (2)
             April 1998                                       Two (2)
             May 1998                                         Two (2)
             June 1998                                        One (1)
             July 1998                                        Two (2)
             September 1998                                   Two (2)

                                Block C Aircraft
                                ----------------
             February 1999                                    Four (4)
             May 1999                                         Four (4)
             July 1999                                        Four (4)
             August 1999                                      One (1)
             September 1999                                   Three (3)

                                Block D Aircraft
                                ----------------
             November 1999                                    Two (2)
             December 1999                                    One (1)
             January 2000                                     One (1)
             March 2000                                       Four (4)
             July 2000                                        Four (4)
             September 2000                                   Three (3)

                                Block E Aircraft
                                ----------------
             January 2001                                     Three (3)
             March 2001                                       Three (3)
             July 2001                                        Three (3)
             September 2001                                   Three (3)
</TABLE>




P.A. No. 1810                         15-1
K/SWA

<PAGE>   12

<TABLE>
<S>          <C>                <C>                  <C>
                                Block F Aircraft
                                ----------------
             October 1998                                     One (1)
             November 1998                                    Two (2)
             December 1998                                    Two (2)

                                Block G Aircraft
                                ----------------
             March 1999                                       Two (2)

                                Block H Aircraft
                                ----------------
             June 1999                                        Two (2)
             July 1999                                        One (1)
             August 1999                                      One (1)
             September 1999                                   Two (2)
             October 1999                                     One (1)
             April 2000                                       Three (3)
             October 2000                                     Three (3)
             April 2001                                       Three (3)
             October 2001                                     Three (3)

                                Block I Aircraft
                                ----------------
             January 2002                                     Four (4)
             March 2002                                       Four (4)
             April 2002                                       Two (2)
             July 2002                                        Four (4)
             October 2002                                     Four (4)

                                Block J Aircraft
                                ----------------
             January 2003                                     Four (4)
             March 2003                                       One (1)

                                Block K Aircraft
                                ----------------
             April 2004                                       Two (2)
             July 2004                                        Three (3)
</TABLE>


P.A. No. 1810                         15-2
K/SWA

<PAGE>   13

<TABLE>
<S>          <C>                <C>                  <C>
                                Block L Aircraft
                                ----------------
             October 1999                                     One (1)
             November 1999                                    Two (2)
             December 1999                                    One (1)
             June 2000                                        Three (3)
             July 2000                                        One (1)
             August 2000                                      Two (2)
             November 2000                                    Two (2)
             December 2000                                    One (1)
             July 2001                                        One (1)
             September 2001                                   One (1)
             October 2001                                     One (1)
             September 2002                                   Three (3)
</TABLE>


         2.2 Notice of Target Delivery Date. Boeing will give Buyer notice of
the Target Delivery Date of the Aircraft approximately 30 days prior to the
scheduled month of delivery.

         2.3 Notice of Delivery Date. If Boeing gives Buyer at least 7 days'
notice of the delivery date of the Aircraft, and an Aircraft delivery is delayed
beyond such delivery date due to the responsibility of Buyer, Buyer will
reimburse Boeing for all costs incurred by Boeing as a result of such delay,
including amounts for storage, insurance, Taxes, preservation or protection of
the Aircraft and interest on payments due.

         2.4 Place of Delivery. The Aircraft will be delivered at an airport
facility selected by Boeing in the State of Washington, unless mutually agreed
otherwise.

         2.5 Title and Risk of Loss. Title to and risk of loss of an Aircraft
will pass from Boeing to Buyer upon delivery of such Aircraft, but not prior
thereto.

         2.6 Bill of Sale. Upon delivery of an Aircraft Boeing will deliver to
Buyer a bill of sale conveying good title to such Aircraft, free of all liens,
claims, charges and encumbrances of every kind whatsoever, and such other
appropriate documents of title as Buyer may reasonably request.


P.A. No. 1810                         15-3
K/SWA

<PAGE>   14

ARTICLE 3. Price of Aircraft.

         3.1 Definitions.

                  3.1.1 Special Features are the features incorporated in
Exhibit A which have been selected by Buyer.

                  3.1.2 Base Aircraft Price is the Aircraft Basic Price
excluding the price of Special Features.

                  3.1.3 Aircraft Basic Price is comprised of the Base Aircraft
Price and the price of the Special Features.

                  3.1.4 Economic Price Adjustment is the adjustment to the
Aircraft Basic Price (Base Aircraft and Special Features) as calculated pursuant
to Exhibit D.

                  3.1.5 Aircraft Price is the total amount Buyer is to pay for
the Aircraft at the time of delivery.

         3.2 Aircraft Basic Price ***.

                  The Aircraft Basic Price, expressed in July 1992 dollars, is
set forth below:

<TABLE>
<CAPTION>
                                 Base                            Special                            Aircraft
                                 Aircraft Price                  Features                           Basic Price
<S>                             <C>                              <C>                                <C>
Block A, B, C,
D & E Aircraft                   ***                             ***                                ***
Block F & G
Aircraft                         ***                             ***                                ***
Block H
Aircraft                         ***                             ***                                ***
Block I
Aircraft                         ***                             ***                                ***
Block J
Aircraft                         ***                             ***                                ***
Block K
Aircraft                         ***                             ***                                ***
Block L Aircraft
                                 ***                             ***                                ***
</TABLE>



         3.3 Aircraft Price. The Aircraft Price will be established at the time
of delivery of such Aircraft to Buyer and will be the sum of:

                  3.3.1 the Aircraft Basic Price, which is *** for the Block A,
B, C, D and E Aircraft, *** for the Block F and G Aircraft, *** for the Block H
Aircraft, *** for the


P.A. No. 1810                         15-4
K/SWA

<PAGE>   15

Block I Aircraft, *** for the Block J Aircraft, *** for the Block K Aircraft and
*** for the Block L Aircraft; plus

                  3.3.2 the Economic Price Adjustments for the Aircraft Basic
Price, as calculated pursuant to the formulas set forth in Exhibit D (Price
Adjustments Due to Economic Fluctuations - Aircraft); plus

                  3.3.3 other price adjustments made pursuant to this Agreement
or other written agreements executed by Boeing and Buyer.

         3.4 Advance Payment Base Price.

                  3.4.1 Advance Payment Base Price. For advance payment
purposes, the following estimated delivery prices of the Aircraft (Advance
Payment Base Price) have been established, using currently available forecasts
of the escalation factors used by Boeing as of the date of signing this
Agreement. The Advance Payment Base Price of each Aircraft is set forth below:

<TABLE>
<CAPTION>
             Month and Year of                                Advance Payment Base
             Scheduled Delivery                               Price per Aircraft
             ------------------                               --------------------

<S>                           <C>                             <C>
                              Block A Aircraft ***
                              ----------------
             October 1997                                            ***
             November 1997                                           ***

                              Block B Aircraft ***
                              ----------------
             January 1998                                            ***
             February 1998                                           ***
             March 1998                                              ***
             April 1998                                              ***
             May 1998                                                ***
             June 1998                                               ***
             July 1998                                               ***
             September 1998                                          ***

                              Block C Aircraft ***
                              ----------------
             February 1999                                           ***
             May 1999                                                ***
             July 1999                                               ***
             August 1999                                             ***
             September 1999                                          ***


</TABLE>

P.A. No. 1810                         15-5
K/SWA

<PAGE>   16
                              Block D Aircraft ***
                              ----------------
<TABLE>
<S>                                                                  <C>
             November 1999                                           ***
             December 1999                                           ***
             January 2000                                            ***
             March 2000                                              ***
             July 2000                                               ***
             September 2000                                          ***

                              Block E Aircraft ***
                              ----------------
             January 2001                                            ***
             March 2001                                              ***
             July 2001                                               ***
             September 2001                                          ***

                              Block F Aircraft ***
                              ----------------
             October 1998                                            ***
             November 1998                                           ***
             December 1998                                           ***

                              Block G Aircraft ***
                              ----------------
             March 1999                                              ***

                              Block H Aircraft ***
                              ----------------
             June 1999                                               ***
             July 1999                                               ***
             August 1999                                             ***
             September 1999                                          ***
             October 1999                                            ***
             April 2000                                              ***
             October 2000                                            ***
             April 2001                                              ***
             October 2001                                            ***

                              Block I Aircraft ***
                              ----------------
             January 2002                                            ***
             March 2002                                              ***
             April 2002                                              ***
             July 2002                                               ***
             October 2002                                            ***

                              Block J Aircraft ***
                              ----------------
             January 2003                                            ***
             March 2003                                              ***


</TABLE>

P.A. No. 1810                         15-6
K/SWA

<PAGE>   17
                              Block K Aircraft ***
                              --------------------
<TABLE>
<S>          <C>              <C>                             <C>
             April 2004                                           ***
             July 2004                                            ***

                              Block L Aircraft ***
                              --------------------
             October 1999                                         ***
             November 1999                                        ***
             December 1999                                        ***
             June 2000                                            ***
             July 2000                                            ***
             August 2000                                          ***
             November 2000                                        ***
             December 2000                                        ***
             July 2001                                            ***
             September 2001                                       ***
             October 2001                                         ***
             September 2002                                       ***
</TABLE>



                  3.4.2 Adjustment of Advance Payment Base Prices - Long-Lead
Aircraft. For Aircraft scheduled for delivery 36 months or more after the date
of this Agreement, the Advance Payment Base Prices appearing in Article 3.4.1
will be used to determine the amount of the first advance payment to be made by
Buyer on the Aircraft. No later than 25 months before the scheduled month of
delivery of each affected Aircraft, Boeing will increase or decrease the Advance
Payment Base Price of such Aircraft as required to reflect the effects of (i)
any adjustments in the Aircraft Basic Price pursuant to this Agreement and (ii)
the then-current forecasted escalation factors used by Boeing. Boeing will
provide the adjusted Advance Payment Base Prices for each affected Aircraft to
Buyer, and the advance payment schedule will be considered amended to substitute
such adjusted Advance Payment Base Prices.



P.A. No. 1810                         15-7
K/SWA

<PAGE>   18


6-1162-RLL-933R7


Southwest Airlines Co.
P.O. Box 36611 - Love Field
Dallas, Texas  75235

Subject:     Letter Agreement No. 6-1162-RLL-933R7 to
             Purchase Agreement No. 1810 -
             Option Aircraft


This Letter Agreement amends Purchase Agreement No. 1810 dated as of January 19,
1994 (the Agreement) between The Boeing Company (Boeing) and Southwest Airlines
Co. (Buyer) relating to Model 737-7H4 aircraft (Aircraft).

All terms used and not defined herein will have the same meaning as in the
Agreement.

In consideration of the purchase by Buyer of the Aircraft, Boeing hereby agrees
to manufacture and sell to Buyer sixty-two (62) additional Model 737-7H4
aircraft as described in paragraph 1 of Attachment A hereto (Option Aircraft)
and fifty-two (52) Model 737-7H4 Rollover Option Aircraft (Rollover Option
Aircraft), subject to the terms and conditions set forth below.

1.       Delivery of Option Aircraft.

         The Option Aircraft will be delivered to Buyer during or before the
months set forth in the following schedule:

--------------------------------------------------------------------------------

***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   19

Southwest Airlines Co.
6-1162-RLL-933R7   Page 2



<TABLE>
<CAPTION>
                                                     Number of                Option
             Month and Year                          Option                   Aircraft
             of Delivery                             Aircraft                 Block
             --------------                          --------                 --------

<S>                                                  <C>                      <C>
             March 2003                              Three  (3)                    M
             April 2003                              Two   (2)                     M
             July 2003                               Four  (4)                     M
             October 2003                            Four  (4)                     M

             January 2004                            Four (4)                      N
             March 2004                              One (1)                       N
             April 2004                              One   (1)                     N
             August 2004                             Two   (2)                     N
             September 2004                          Three (3)                     N
             October 2004                            Two   (2)                     N
</TABLE>

<TABLE>
<CAPTION>
                                                     Number of                Option
             Month and Year                          Option                   Aircraft
             of Delivery                             Aircraft                 Block
             --------------                          --------                 ------

<S>                                                  <C>                      <C>
             January 2005                            Four (4)                    O
             March 2005                              Four (4)                    O
             April 2005                              Two (2)                     O
             July 2005                               Four (4)                    O
             October 2005                            Four (4)                    O

             January 2006                            Four (4)                    P
             March 2006                              Four (4)                    P
             April 2006                              Two (2)                     P
             July 2006                               Four (4)                    P
             October 2006                            Four (4)                    P
</TABLE>


2.       Delivery of Rollover Option Aircraft.

         2.1 The Rollover Option Aircraft will be delivered to Buyer during or
before the years set forth in the following schedule:

<TABLE>
<CAPTION>
                                                                              Option
             Year of                   Number of                              Aircraft
             Delivery                  Option Aircraft                        Block
             --------                  ---------------                        --------

<S>                                    <C>                                    <C>
             2007                      Twenty (20)                                 Q
             2008                      Twenty (20)                                 R
             2009                      Twelve (12)                                 S
</TABLE>

         2.2 The fifty-two (52) Rollover Option Aircraft are offered to Buyer
subject to the following conditions:


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   20

Southwest Airlines Co.
6-1162-RLL-933R7   Page 3

                  2.2.1 Buyer can exercise any fifty-two (52) of the sixty-two
(62) Option Aircraft, and will be offered a Rollover Option Aircraft for each
option aircraft exercised up to and including fifty-two (52).

                  2.2.2 Conversely to Article 2.2.1 above, if Buyer does not
exercise a minimum of fifty-two (52) Option Aircraft, one Rollover Option
Aircraft will be deleted for each Option Aircraft not exercised by Buyer.

                  2.2.3 When Buyer exercises one or more Option Aircraft, Boeing
will offer the same quantity of Rollover Option Aircraft to Buyer in the years
identified in Article 2.1 above.

                  2.2.4 The Rollover Option Aircraft delivery month offered by
Boeing to Buyer will be at least 24 months from the Option exercise date of the
corresponding option.

                  2.2.5 When Boeing offers the Rollover Option Aircraft to
Buyer, Buyer will accept such Rollover Option Aircraft by wire transferring
$100,000 to Boeing. In the event Buyer exercises its option to purchase the
Rollover Option Aircraft, such application will be in accordance with Article
4.1 herein.

3.       Price.

         3.1 The advance payment base prices of the Option Aircraft set forth
below and in paragraph 2.1 of Attachment A represent the estimated delivery
prices of the Option Aircraft. The Option Aircraft pricing elements and
associated pricing terms and conditions are given in Attachment A.

         3.2 Price and escalation provisions for Model 737-7H4 aircraft
delivering after 2002, are not currently available. The estimated Advance
Payment Base Prices shown in paragraph 3.3 below and in paragraph 2.1 of
Attachment A are based on currently available price and escalation provisions.
As price and escalation provisions become available for Model 737-7H4 aircraft
delivering after 2002, such price and escalation provisions will be
appropriately applied to the applicable Option Aircraft.

For additional information relating to price and escalation provisions
applicable to Option Aircraft delivering after 2002 refer to paragraphs 2.2 and
3.2 of Attachment A.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   21

Southwest Airlines Co.
6-1162-RLL-933R7   Page 4

         3.3 The Advance Payment Base Prices of the Option Aircraft indicated
below do include an amount for special features in addition to those
specifically described in Attachment A but do not include any amount for items
of Buyer Furnished Equipment (BFE). An estimate for typical special features is
*** per Aircraft (expressed in 1992 STE dollars) and for BFE is *** per Aircraft
(expressed in delivery year dollars).

<TABLE>
<CAPTION>
             Month and Year                              Advance Payment Base
             of Delivery                                 Price per Option Aircraft
             --------------                              -------------------------

<S>                            <C>                       <C>
                               Block M Aircraft***
                               -------------------
             March 2003
             April 2003
             July 2003
             October 2003

                               Block N Aircraft***
                               -------------------
             January 2004
             March 2004
             April 2004
             August 2004
             September 2004
             October 2004

                               Block O Aircraft***
                               -------------------
             January 2005
             March 2005
             April 2005
             July 2005
             October 2005

                               Block P Aircraft***
                               -------------------
             January 2006
             March 2006
             April 2006
             July 2006
             October 2006
</TABLE>


         3.4 The Option Aircraft purchase price will be the applicable basic
price thereof at the time of Option Aircraft delivery adjusted in accordance
with Boeing's Aircraft escalation provisions contained in the definitive
agreement to purchase the Option Aircraft. The purchase price will include the
price for Seller Purchased Equipment (SPE) if Buyer has


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   22

Southwest Airlines Co.
6-1162-RLL-933R7   Page 5

elected to change Buyer Furnished Equipment (BFE) to SPE.

4.       Option Aircraft Payment.

         4.1 In consideration of the granting of the option as set forth herein,
on or before the date Boeing and Buyer enter into a definitive agreement to
purchase the Aircraft, Buyer will pay a deposit to Boeing of $100,000 for each
Option Aircraft (Deposit). In the event Buyer exercises its option herein, the
amount of the Deposit will be credited against the first advance payment due for
such Option Aircraft pursuant to the advance payment schedule set forth in
paragraph 3 of Attachment A. The Deposits for the Option Aircraft will be
refunded to Buyer, without interest, if the parties do not enter into a
definitive Agreement for the Aircraft.

In the event that, after the parties enter into a definitive agreement to
purchase the Aircraft, Buyer does not exercise its option to purchase the Option
Aircraft pursuant to the terms and conditions set forth herein, Boeing will be
entitled to retain the Deposits for the Option Aircraft except as provided in
paragraphs 6 herein.

         4.2 Advance payments in the amount of 30% of the advance payment base
price will be payable on the Option Aircraft in accordance with paragraph 3 of
Attachment A. The remainder of the Option Aircraft purchase price is due at the
time of delivery of the Option Aircraft.

5.       Option Exercise.

         5.1 To exercise its Option, Buyer will give written or telegraphic
notice thereof to Boeing on or before eighteen (18) months prior to the first
day of the delivery month of each Option Aircraft.

In such notice Buyer will select the Option Model type, and the applicable
delivery positions.

         5.2 It is understood and agreed that Boeing may accelerate the option
exercise dates specified above if Boeing must make production decisions which
are dependent on Buyer's decision to buy the Option Aircraft. If Boeing elects
to accelerate the option exercise dates, Boeing will do so by giving written or
telegraphic notice thereof to Buyer. Such notice will specify the revised option
exercise dates, which will not be earlier than 30 days after the date of


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   23

Southwest Airlines Co.
6-1162-RLL-933R7   Page 6


transmittal of such notice, and the Option Aircraft delivery positions affected
by such revision. If Buyer fails to exercise its option for any Option Aircraft
affected by such revised dates, the Deposit applicable to such Option Aircraft
will be promptly refunded, with interest, to Buyer. The interest rate for
calculation of the interest associated with such refund is the rate of two
percent (2%) below the Citibank base rate in effect from time to time during the
period the option deposit is held by Boeing.

6.       Contract Terms.

         It is understood that Boeing and Buyer will use their best efforts to
enter into a definitive agreement for the Option Aircraft within thirty (30)
days after Buyer exercises an option to purchase Option Aircraft pursuant to
paragraph 5 covering the detailed terms and conditions for the sale of such
Option Aircraft.

Such definitive agreement will include the terms and conditions contained herein
together with the terms and conditions, not inconsistent herewith, contained in
Boeing's then-current standard form of purchase agreement for the sale of Model
737-700 aircraft in effect as of the date of option exercise and such additional
terms and conditions as may be mutually agreed upon. In the event the parties
have not entered into such an agreement within the time period contemplated
herein, either party may, exercisable by written or telegraphic notice given to
the other within thirty (30) days after such period, terminate the purchase of
such Option Aircraft.

7.       Termination of Option to Purchase.

         Either Boeing or Buyer may terminate the option to purchase an Option
Aircraft if any of the following events are not accomplished by the respective
dates contemplated in this letter agreement, or in the Agreement, as the case
may be:

         (i) termination of the purchase of the Aircraft under the Agreement for
any reason;

         (ii) payment by Buyer of the Deposit with respect to an Option Aircraft
pursuant to paragraph 4.1 herein;

         (iii) exercise of an option to purchase an Option Aircraft pursuant to
the terms hereof. Any termination of an option to purchase by Boeing which is
based on the termination of the purchase of


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   24

Southwest Airlines Co.
6-1162-RLL-933R7   Page 7


Aircraft under the Agreement will be on a one-for-one basis, for each Aircraft
so terminated.

Any cancellation of an option to purchase which is based on failure to make the
required Deposit or to exercise the option to purchase shall only apply to the
Option Aircraft so canceled.

Termination of an option to purchase provided by this letter agreement will be
caused by either party giving written notice to the other within 10 days after
the applicable date. Upon receipt of such notice, all rights and obligations of
the parties with respect to an Option Aircraft for which the option to purchase
has been terminate will thereupon terminate.

If termination is result of a revision of an option exercise date by Boeing
pursuant to paragraph 5.2, Boeing will promptly refund to Buyer, without
interest, any payments received from Buyer, including the Deposit, with respect
to the Option Aircraft for which the option is terminated. If termination is for
any other reason, Boeing will promptly refund to Buyer, without interest, any
payments received from Buyer with respect to the affected Option Aircraft,
except the Deposit, which Buyer may apply to any model Boeing aircraft purchased
by Buyer from Boeing at a future date.

8. Confidential Treatment. Buyer understands that certain commercial and
financial information contained in this Letter Agreement including any
attachments hereto is considered by Boeing as confidential. Buyer agrees that it
will treat this Letter Agreement and the


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   25

Southwest Airlines Co.
6-1162-RLL-933R7   Page 8


information contained herein as confidential and will not, without the prior
written consent of Boeing, disclose this Letter Agreement or any information
contained herein to any other person or entity except as provided in Letter
Agreement No. 6-1162-RLL-934R1.

Very truly yours,

THE BOEING COMPANY



By:    /s/ DAWN S. FOSTER
    ------------------------

Its:    ATTORNEY-IN-FACT
     ------------------------



ACCEPTED AND AGREED TO this

date: March 30, 1999

SOUTHWEST AIRLINES CO.



By:  /s/ LAURA WRIGHT
    ------------------------


Its:   TREASURER
     ------------------------


Attachments



P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   26


Attachment A to
6-1162-RLL-933R7
Page 1


Model 737-7H4 Aircraft

1. Option Aircraft Description and Changes.

         1.1 Aircraft Description. The Option Aircraft is described by Boeing
Detail Specification D6-38808-1, Dated October 30 ,1996.

         1.2 Changes. The Detail Specification will be revised to include:

                  (1) Changes applicable to the basic Model 737-700 aircraft
which are developed by Boeing between the date of the Detail Specification and
the signing of a definitive agreement to purchase the Option Aircraft.

                  (2) Changes mutually agreed upon.

                  (3) Changes required to obtain a Standard Certificate of
Airworthiness.

                  (4) To provide sufficient Option Aircraft manufacturing and
procurement lead time it is necessary for Boeing and Buyer to reach final
agreement on the Option Aircraft configuration, including BFE/SPE vendor
selection fifteen (15) months prior to delivery of each Option Aircraft. If such
items are not resolved by the indicated dates, Boeing reserves the right to
amend this letter agreement:

                           (i) to adjust the scheduled delivery of the Option
Aircraft to a later time period and,

                           (ii) to make such other changes as are appropriate
and consistent with the revised Option Aircraft deliveries.

         1.3 Effect of Changes. Changes to the Detail Specification incorporated
pursuant to the provisions of the clauses above will include the effects of such
changes upon Option Aircraft weight, balance, design and performance.
Performance guarantees for the Option Aircraft which are mutually acceptable to
the parties will be included in the definitive agreement for the Option
Aircraft.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   27


Attachment A to
6-1162-RLL-933R7
Page 2



2.       Price Description

         2.1 Price Elements Per Aircraft


<TABLE>
<CAPTION>
                    1                 2            3
                    -                 -            -

                 AIRCRAFT &                                  ADV. PMT.
AIRCRAFT      ESTIMATED SPECIAL                ESTIMATED    BASE PRICE
DELIVERY      FEATURES PRICE     ESTIMATED     ESCALATION   (Elements)
MO. & YR.      (JULY 1992$)      ESCALATION     SHARING     1 + 2 + 3
---------     -----------------  ----------   -----------   ----------

<S>           <C>                 <C>         <C>           <C>
BLOCK M
-------

March 2003          ***              ***          -***          ***
April 2003          ***              ***          -***          ***
July 2003           ***              ***          -***          ***
October 2003        ***              ***          -***          ***

BLOCK N
-------

January 2004        ***              ***          -***          ***
March 2004          ***              ***          -***          ***
April 2004          ***              ***          -***          ***
August 2004         ***              ***          -***          ***
September 2004      ***              ***          -***          ***
October 2004        ***              ***          -***          ***

BLOCK O
-------

January 2005        ***              ***          -***          ***
March 2005          ***              ***          -***          ***
April 2005          ***              ***          -***          ***
July 2005           ***              ***          -***          ***
October 2005        ***              ***          -***          ***

BLOCK P
-------

January 2006        ***              ***          -***          ***
March 2006          ***              ***          -***          ***
April 2006          ***              ***          -***          ***
July 2006           ***              ***          -***          ***
October 2006        ***              ***          -***          ***
</TABLE>



P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   28


Attachment A to
6-1162-RLL-933R7
Page 3


2. Price Description. (Continued)

                  2.2 Price Adjustments For Option Aircraft Delivering From
                  March 2003 through December 2009.

                  2.2.1 Special Features. The price for Special Features
incorporated in the Option Aircraft Detail Specification will be adjusted to
Boeing's then-current prices for such features as of the date of execution of
the definitive agreement for the Option Aircraft.

                  2.2.2 Escalation Adjustments. For escalation provisions
applicable to Option Aircraft delivering after 2002, see paragraph 2.2.6 below.

                  2.2.3 Base Price Adjustments for FAA Changes. The Aircraft
Basic Price of the Option Aircraft will be adjusted for any FAA mandated changes
incorporated into the Aircraft.

                  2.2.4 Price Adjustments for Changes. Boeing may adjust the
Aircraft Basic Price and the Advance Payment Base Price for any changes mutually
agreed upon subsequent to the date that Buyer and Boeing enter into a definitive
agreement for the Option Aircraft.

                  2.2.5 Base Price Adjustments. The Aircraft Basic Price of the
Option Aircraft will be adjusted to Boeing's then-current prices as of the date
of execution of the definitive agreement for the Option Aircraft in accordance
with the agreement reached below. The Aircraft Basic Price starting point for
options delivering in 2003 is *** (July 1992 STE), for options delivering in
2004 is *** (July 1992 STE), for options delivering in 2005 through 2009 is ***
(July 1992 STE). Such Aircraft Basic Price may increase in accordance with
paragraphs 2.2.1, 2.2.2, 2.2.3 and 2.2.4. For any other changes to the Aircraft
Basic Price, Boeing may increase the Aircraft Basic Price by a maximum of ***
(July 1992 STE) for Aircraft delivering in 2005 and by a maximum of *** (July
1992 STE) per year or portion thereof starting in January 2006.

                  2.2.6 Prices for Long Lead Time Aircraft. Boeing has not
established escalation provisions for Model 737-700 aircraft for delivery 2003
and after. Such escalation provisions (i) will be incorporated into the Option
Aircraft definitive agreement when such information is available and (ii) will
be the then-current escalation provisions applicable to the same model aircraft
and engines delivering in the same time period as the Option Aircraft. The
resulting revisions to the definitive agreement will

P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   29


Attachment A to
6-1162-RLL-933R7
Page 4


include but not be limited to, adjustment of the Aircraft Basic Price of the
Option Aircraft, the Advance Payment Base Price, the Aircraft escalation
provisions and the advance payment amounts due on the Option Aircraft.

                  2.2.7 BFE to SPE. An estimate of the total price for items of
Buyer Furnished Equipment (BFE) changed to Seller Purchased Equipment (SPE)
pursuant to the Configuration Specification is included in the Option Aircraft
price build-up. The purchase price of the Option Aircraft will be adjusted by
the price charged to Boeing for such items plus 10% of such price. If all BFE
except developmental avionics is converted to SPE, Boeing will waive the 10%
fee.

3. Advance Payment Schedules, Prices and Adjustments.

         3.1 Buyer will pay to Boeing advance payments for the Option Aircraft
on the dates and in the amounts determined below.



P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   30


Attachment A to
6-1162-RLL-933R7
Page 2


<TABLE>
<CAPTION>
                                                                 Amount Due per Aircraft
                                                                 -----------------------
                                                                    (Percentage times
Due Date of Payment                                            Advance Payment Base Price)
-------------------

<S>                                                            <C>
Deposit                                                              100,000 (if applicable)

18 months prior to the first                                         15% (less the
day of the scheduled delivery                                             Deposit if any)
month of the Aircraft

12 months prior to the first                                         5%
day of the scheduled delivery
month of the Aircraft

9 months prior to the first                                          5%
day of the scheduled delivery
month of the Aircraft

6 months prior to the first                                          5%
day of the scheduled delivery
month of the Aircraft
                                                                   ---

                    Total                                          30%
</TABLE>

Any advance payments that would be past due as of the date of signing the
definitive purchase agreement for the Option Aircraft in accordance with the
above schedule are due and payable on such date.

         3.2 Option Aircraft advance payment base prices will be increased or
decreased, as appropriate, at the time of signing of the definitive purchase
agreement for the Option Aircraft, using the then-current forecasted aircraft
escalation factors used by Boeing, to determine the amount of the advance
payments to be made by Buyer on the Option Aircraft.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   31


Attachment B to
6-1162-RLL-933R7
Page 1


                             PRICE ADJUSTMENT DUE TO
                              ECONOMIC FLUCTUATIONS
                            AIRCRAFT PRICE ADJUSTMENT
                             (July 1992 Base Price)


1. Formula.

         The Aircraft Price Adjustment will be determined at the time of
Aircraft delivery in accordance with the following formula:

         Pa = (P)(L + M - 1)

         Where:

         Pa = Aircraft Price Adjustment.

         L = .65 x  ECI
                   -----
                   116.2

         M = .35 x  ICI
                   -----
                   115.9

         P = Aircraft Basic Price (as set forth in Article 3.2 of this
             Agreement).

       ECI = A value using the "Employment Cost Index for workers in aerospace
             manufacturing" (aircraft manufacturing, standard industrial
             classification code 3721, compensation, base month and year June
             1989 = 100), as released by the Bureau of Labor Statistics, U.S.
             Department of Labor on a quarterly basis for the months of March,
             June, September and December, calculated as follows: A three-month
             arithmetic average value (expressed as a decimal and rounded to the
             nearest tenth) will be determined using the months set forth in the
             table below for the applicable Aircraft, with the released
             Employment Cost Index value described above for the month of March
             also being used for the months of January and February; the value
             for June also used for April and May; the value for September also
             used for July and August; and the value for December also used for
             October and November.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   32


Attachment B to
6-1162-RLL-933R7
Page 2


       ICI = The three-month arithmetic average of the released monthly values
             for the Industrial Commodities Index as set forth in the "Producer
             Prices and Price Index" (Base Year 1982 = 100) as released by the
             Bureau of Labor Statistics, U.S. Department of Labor values
             (expressed as a decimal and rounded to the nearest tenth) for the
             months set forth in the table below for the applicable Aircraft.

         In determining the value of L, the ratio of ECI divided by 116.2 will
be expressed as a decimal rounded to the nearest ten-thousandth and then
multiplied by .65 with the resulting value also expressed as a decimal and
rounded to the nearest ten-thousandth.

         In determining the value of M, the ratio of ICI divided by 115.9 will
be expressed as a decimal rounded to the nearest ten-thousandth and then
multiplied by .35 with the resulting value also expressed as a decimal and
rounded to the nearest ten-thousandth.

<TABLE>
<CAPTION>
                                Months to be Utilized
Month of Scheduled              in Determining the
Aircraft Delivery               Value of ECI and ICI
-----------------               -------------------------

<S>                             <C>
January                         June  B, July  B, Aug.  B
February                        July  B, Aug.  B, Sept. B
March                           Aug.  B, Sept. B, Oct.  B
April                           Sept. B, Oct.  B, Nov.  B
May                             Oct.  B, Nov.  B, Dec.  B
June                            Nov.  B, Dec.  B, Jan.  D
July                            Dec.  B, Jan.  D, Feb.  D
August                          Jan.  D, Feb.  D, Mar.  D
September                       Feb.  D, Mar.  D, Apr.  D
October                         Mar.  D, Apr.  D, May   D
November                        Apr.  D, May   D, June  D
December                        May   D, June  D, July  D
</TABLE>

The following definitions of B and D will apply:

             B = The calendar year before the year in which the
                 scheduled month of delivery as set forth in Paragraph 1
                 occurs.

             D = The calendar year during which the scheduled month of
                 delivery as set forth in Paragraph 1 occurs.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   33


Attachment B to
6-1162-RLL-933R7
Page 3


2. If at the time of delivery of an Aircraft Boeing is unable to determine the
Aircraft Price Adjustment because the applicable values to be used to determine
the ECI and ICI have not been released by the Bureau of Labor Statistics, then:

         2.1 The Aircraft Price Adjustment, to be used at the time of delivery
of each of the Aircraft, will be determined by utilizing the escalation
provisions set forth above. The values released by the Bureau of Labor
Statistics and available to Boeing 30 days prior to scheduled Aircraft delivery
will be used to determine the ECI and ICI values for the applicable months
(including those noted as preliminary by the Bureau of Labor Statistics) to
calculate the Aircraft Price Adjustment. If no values have been released for an
applicable month, the provisions set forth in Paragraph 2.2 below will apply. If
prior to delivery of an Aircraft the U.S. Department of Labor changes the base
year for determination of the ECI or ICI values as defined above, such rebased
values will be incorporated in the Aircraft Price Adjustment calculation. The
payment by Buyer to Boeing of the amount of the Purchase Price for such
Aircraft, as determined at the time of Aircraft delivery, will be deemed to be
the payment for such Aircraft required at the delivery thereof.

         2.2 If prior to delivery of an Aircraft the U.S. Department of Labor
substantially revises the methodology used for the determination of the values
to be used to determine the ECI and ICI values (in contrast to benchmark
adjustments or other corrections of previously released values), or for any
reason has not released values needed to determine the applicable Aircraft Price
Adjustment, the parties will, prior to delivery of any such Aircraft, select a
substitute for such values from data published by the Bureau of Labor Statistics
or other similar data reported by non-governmental United States organizations,
such substitute to lead in application to the same adjustment result, insofar as
possible, as would have been achieved by continuing the use of the original
values as they may have fluctuated during the applicable time period.
Appropriate revision of the formula will be made as required to reflect any
substitute values. However, if within 24 months from delivery of the Aircraft
the Bureau of Labor Statistics should resume releasing values for the months
needed to determine the Aircraft Price Adjustment, such values will be used to
determine any increase or decrease in the Aircraft Price Adjustment for the
Aircraft from that determined at the time of delivery of such Aircraft.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   34


Attachment B to
6-1162-RLL-933R7
Page 4


         2.3 In the event escalation provisions are made non-enforceable or
otherwise rendered null and void by any agency of the United States Government,
the parties agree, to the extent they may lawfully do so, to equitably adjust
the Purchase Price of any affected Aircraft to reflect an allowance for
increases or decreases in labor compensation and material costs occurring since
February, 1992, which is consistent with the applicable provisions of paragraph
1 of this Exhibit D.

3. For the calculations herein, the values released by the Bureau of Labor
Statistics and available to Boeing 30 days prior to scheduled Aircraft delivery
will be used to determine the ECI and ICI values for the applicable months
(including those noted as preliminary by the Bureau of Labor Statistics) to
calculate the Aircraft Price Adjustment.

Note:    Any rounding of a number, as required under this Exhibit D with respect
         to escalation of the airframe price, will be accomplished as follows:
         if the first digit of the portion to be dropped from the number to be
         rounded is five or greater, the preceding digit will be raised to the
         next higher number.


P.A. No. 1810
K/SWA                                                                       SA-8

<PAGE>   35
                                                                    EXHIBIT 10.1

                          Supplemental Agreement No. 9

                                       to

                           Purchase Agreement No. 1810

                                     between

                               The Boeing Company

                                       and

                             SOUTHWEST AIRLINES CO.

                    Relating to Boeing Model 737-7H4 Aircraft


         THIS SUPPLEMENTAL AGREEMENT, entered into as of April 29, 1999, by and
between THE BOEING COMPANY, a Delaware corporation with its principal offices in
Seattle, Washington, (Boeing) and SOUTHWEST AIRLINES CO., a Texas corporation
with its principal offices in City of Dallas, State of Texas (Buyer);

         WHEREAS, the parties hereto entered into Purchase Agreement No. 1810
dated January 19, 1994, relating to Boeing Model 737-7H4 aircraft (the
Agreement) and;

         WHEREAS, Buyer has agreed to exercise the option to purchase six (6)
additional Option Aircraft and to accelerate delivery of those Option Aircraft
from July 2006 (2) and October 2006 four (4) to September 2000 (1), October 2000
(1), November 2000 (1), December 2000 (1), January 2001 (1) and February 2001
(1);

         NOW THEREFORE, in consideration of the mutual covenants herein
contained, the parties agree to amend the Agreement as follows:


--------------------------------------------------------------------------------
***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.


P.A. No. 1810                      SA-9-1
K/SWA


<PAGE>   36


1. The Table of Contents of the Agreement is deleted in its entirety and a new
Table of Contents is attached hereto and incorporated into the Agreement by this
reference.

2. Article 1, entitled "Subject Matter of Sale," paragraph 1.1 entitled "The
Aircraft" is deleted in its entirety and replaced by a new paragraph 1.1 revised
to reflect one hundred forty-two (142) Aircraft. Such new page 1-1 is attached
hereto and incorporated into the Agreement by this reference.

3. Article 2, entitled "Delivery, Title and Risk of Loss," paragraph 2.1,
entitled "Time of Delivery," is deleted in its entirety and replaced by a new
paragraph 2.1 revised to add six (6) Block "L" Aircraft for delivery in
September 2000 (1), October 2000 (1), November 2000 (1), December 2000 (1),
January 2001 (1) and February 2001 (1). Such new pages 2-1, 2-2 and 2-3 are
attached hereto and incorporated into the Agreement by this reference.

4. Article 3, entitled "Price of Aircraft", paragraph 3.4 entitled "Advance
Payment Base Price," subparagraph 3.4.1 entitled "Advance Payment Base Price"
is revised by adding Advance Payment Base Prices for the exercised Block "L"
September 2000, October 2000, November 2000, December 2000, January 2001 and
February 2001 Aircraft, and by revising the Advance Payment Base Prices to
reflect current escalation factors as of the date of this Supplemental
Agreement for the Block "H" April 2001 and October 2001 Aircraft and the Block
"L" November 2000, December 2000, July 2001, September 2001 and October 2001
Aircraft. Such new pages 3-1, 3-2, 3-3 and 3-4 are attached hereto and
incorporated into the Agreement by this reference.

5. Letter Agreement No. 6-1162-RLL-933R7 entitled "Option Aircraft" is deleted
in its entirety and replaced with Letter Agreement No. 6-1162-RLL-933R8 attached
hereto and incorporated herein by this reference. The third paragraph is revised
to refer to forty-six (46) Rollover Option Aircraft. Article 2 entitled
"Delivery of Rollover Option Aircraft," paragraph 2.1 is revised to change the
quantity of Rollover Option Aircraft from twelve (12) to six (6) in the year
2009; paragraph 2.2 and subparagraphs 2.2.1 and 2.2.2 are revised by changing
the quantity of Rollover Option Aircraft from fifty-two (52) to forty-six (46).

6. All references in the Letter Agreements associated with Purchase Agreement
No. 1810 shall be deemed to refer to


P.A. No. 1810                      SA-9-2
K/SWA


<PAGE>   37


the purchase by Buyer of one hundred forty-two (142) Model 737-7H4 Aircraft,
sixty-two (62) Model 737-7H4 Option Aircraft and forty-six (46) Model 737-7H4
Rollover Option Aircraft, to the extent such reference is not specifically
addressed herein.


P.A. No. 1810                      SA-9-3
K/SWA


<PAGE>   38


7. Concurrent with execution of this Supplemental Agreement, Buyer will pay to $
***. Such amount reflects the difference in advance payments due as a result of
the exercise of the Option to purchase six Aircraft, the revision in Advance
Payment Base Price for Aircraft as described above and the deposits due for six
Rollover Option Aircraft converted to Option Aircraft.

The Agreement will be deemed to be supplemented to the extent herein provided
and as so supplemented will continue in full force and effect.

EXECUTED IN DUPLICATE as of the day and year first above written.

THE BOEING COMPANY                      SOUTHWEST aIRLINES cO.



By:    /S/ DAWN S. FOSTER               By:  /S/ LAURA WRIGHT
    ------------------------               -------------------------------------

Its:    ATTORNEY-IN-FACT                Its: TREASURER
     -----------------------                ------------------------------------


P.A. No. 1810                      SA-9-4
K/SWA


<PAGE>   39


                               PURCHASE AGREEMENT

                                     between

                               THE BOEING COMPANY

                                       and

                             SOUTHWEST AIRLINES CO.






                    Relating to Boeing Model 737-7H4 Aircraft

                         Purchase Agreement Number 1810







--------------------------------------------------------------------------------
***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.


P.A. No. 1810                         15-1
K/SWA


<PAGE>   40


                                TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                        Page            SA
                                                                      Number        Number
                                                                      ------        ------
ARTICLES
--------

<S>                                                                   <C>           <C>
1.   Subject Matter of Sale........................................     1-1          SA-9

2.   Delivery, Title and Risk
     of Loss.......................................................     2-1          SA-9

3.   Price of Aircraft.............................................     3-1          SA-9

4.   Taxes.........................................................     4-1

5.   Payment.......................................................     5-1

6.   Excusable Delay...............................................     6-1

7.   Changes to the Detail
     Specification.................................................     7-1          SA-1

8.   Federal Aviation Requirements and
     Certificates and Export License...............................     8-1

9.   Representatives, Inspection,
     Flights and Test Data.........................................     9-1

10.  Assignment, Resale or Lease...................................    10-1

11.  Termination for Certain Events................................    11-1

12.  Product Assurance; Disclaimer and
     Release; Exclusion of Liabilities;
     Customer Support; Indemnification
     and Insurance.................................................    12-1

13.  Buyer Furnished Equipment and
     Spare Parts...................................................    13-1

14.  Contractual Notices and Requests..............................    14-1

15.  Miscellaneous.................................................    15-1
</TABLE>


P.A. No. 1810                         15-2
K/SWA


<PAGE>   41


                                TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                             SA
                                                         Number
                                                         ------

EXHIBITS
--------

<S>         <C>                                           <C>
A           Aircraft Configuration                        SA-1

B           Product Assurance Document                    SA-1

C           Customer Support Document

D           Price Adjustments Due to
            Economic Fluctuations - Aircraft

E           Buyer Furnished Equipment
            Provisions Document

F           Defined Terms Document
</TABLE>


LETTER AGREEMENTS


1810-1      Waiver of Aircraft Demonstration Flight


P.A. No. 1810                         15-3
K/SWA


<PAGE>   42


                                TABLE OF CONTENTS
<TABLE>
<CAPTION>
                                                                      SA
                                                                  Number
                                                                  ------
RESTRICTED LETTER AGREEMENTS
----------------------------

<S>                                                               <C>
6-1162-RLL-932        Promotional Support

6-1162-RLL-933R8      Option Aircraft                              SA-9

6-1162-RLL-934R1      Disclosure of Confidential                   SA-1
                      Information

6-1162-RLL-935R1      Performance Guarantees                       SA-1

6-1162-RLL-936R4      Certain Contractual Matters                  SA-4

6-1162-RLL-937        Alternate Advance Payment Schedule

6-1162-RLL-938         ***

6-1162-RLL-939R1      Certification Flight Test Aircraft           SA-1

6-1162-RLL-940R1      Training Matters                             SA-1

6-1162-RLL-941R1      Other Matters                                SA-1

6-1162-RLL-942        Open Configuration Matters

6-1162-RLL-943R1      Substitution Rights                          SA-6

6-1162-RLL-944        Airframe Maintenance Material Cost
                      Protection Program

6-1162-RLL-945        Comparison of 737-7H4 and 737-3H4
                      Block Fuel Burn

6-1162-RLL-1855R3     Additional Contractual Matters               SA-4

6-1162-RLL-1856        ***                                         SA-1

6-1162-RLL-1857       Service Ready Validation Program             SA-1
                      Field Test

6-1162-RLL-1858R1     Escalation Matters                           SA-4
</TABLE>


P.A. No. 1810                         15-4
K/SWA


<PAGE>   43


                             TABLE OF CONTENTS CON'T

<TABLE>
<CAPTION>
                                                         SA
                                                     Number
                                                     ------
RESTRICTED LETTER AGREEMENTS
----------------------------

<S>                                                  <C>
6-1162-RLL-2036   Amortization of Costs for
                  Customer Unique Changes             SA-1

6-1162-RLL-2037   Reconciliation of the Aircraft      SA-1
                  Basic Price

6-1162-RLL-2073   Maintenance Training Matters        SA-1
</TABLE>


P.A. No. 1810                         15-5
K/SWA


<PAGE>   44


                           PURCHASE AGREEMENT NO. 1810

                                   Relating to

                          BOEING MODEL 737-7H4 AIRCRAFT

                          -----------------------------


         This Agreement is entered into as of January 19th 1994, by and between
The Boeing Company, a Delaware corporation, with its principal office in
Seattle, Washington (Boeing), and Southwest Airlines Co., a Texas corporation,
with its principal office in the City of Dallas, State of Texas (Buyer).


Accordingly, Boeing and Buyer agree as follows:


P.A. No. 1810                         15-6
K/SWA


<PAGE>   45


ARTICLE 1. Subject Matter of Sale.

         1.1 The Aircraft. Subject to the terms and conditions of this
Agreement, Boeing will manufacture and deliver to Buyer and Buyer will purchase
and accept delivery from Boeing of one hundred forty-two (142) Boeing Model
737-7H4 aircraft (the Aircraft) manufactured in accordance with Boeing Detail
Specification D6-38808-1, dated October 30, 1996, as described in Exhibit A, as
modified from time to time in accordance with this Agreement (Detail
Specification).

         1.2 Additional Goods and Services. In connection with the sale of the
Aircraft, Boeing will also provide to Buyer certain other things under this
Agreement, including data, documents, training and services, all as described in
this Agreement.

         1.3 Performance Guarantees. Any performance guarantees applicable to
the Aircraft will be expressly included in this Agreement. Where performance
guarantees are included in this Agreement other than within the Detail
Specification, such guarantees will be treated as being incorporated in the
Detail Specification by this reference.

         1.4 Defined Terms. For ease of use, certain terms are treated as
defined terms in this Agreement. Such terms are identified with a capital letter
and set forth and/or defined in Exhibit F.


P.A. No. 1810                         15-7
K/SWA


<PAGE>   46


ARTICLE 2. Delivery, Title and Risk of Loss.

         2.1 Time of Delivery. The Aircraft will be delivered to Buyer by
Boeing, assembled and ready for flight and Buyer will accept delivery of the
Aircraft, in accordance with the following schedule:

<TABLE>
<CAPTION>
Month and Year
 of Delivery                             Quantity of Aircraft
 -----------                             --------------------

                   Block A Aircraft
                   ----------------
<S>                                              <C>
October 1997                                     Two (2)
November 1997                                    Two (2)
</TABLE>

<TABLE>
<CAPTION>
                   Block B Aircraft
                   ----------------
<S>                                              <C>
January 1998                                     Two (2)
February 1998                                    Three (3)
March 1998                                       Two (2)
April 1998                                       Two (2)
May 1998                                         Two (2)
June 1998                                        One (1)
July 1998                                        Two (2)
September 1998                                   Two (2)
</TABLE>

<TABLE>
<CAPTION>
                   Block C Aircraft
                   ----------------
<S>                                              <C>
February 1999                                    Four (4)
May 1999                                         Four (4)
July 1999                                        Four (4)
August 1999                                      One (1)
September 1999                                   Three (3)
</TABLE>

<TABLE>
<CAPTION>
                   Block D Aircraft
                   ----------------
<S>                                              <C>
November 1999                                    Two (2)
December 1999                                    One (1)
January 2000                                     One (1)
March 2000                                       Four (4)
July 2000                                        Four (4)
September 2000                                   Three (3)
</TABLE>

<TABLE>
<CAPTION>
                   Block E Aircraft
                   ----------------
<S>                                              <C>
January 2001                                     Three (3)
March 2001                                       Three (3)
July 2001                                        Three (3)
September 2001                                   Three (3)
</TABLE>


P.A. No. 1810                         15-8
K/SWA


<PAGE>   47


<TABLE>
<CAPTION>
                   Block F Aircraft
                   ----------------
<S>                                              <C>
October 1998                                     One (1)
November 1998                                    Two (2)
December 1998                                    Two (2)
</TABLE>

<TABLE>
<CAPTION>
                   Block G Aircraft
                   ----------------
<S>                                              <C>
March 1999                                       Two (2)
</TABLE>

<TABLE>
<CAPTION>
                   Block H Aircraft
                   ----------------
<S>                                              <C>
June 1999                                        Two (2)
July 1999                                        One (1)
August 1999                                      One (1)
September 1999                                   Two (2)
October 1999                                     One (1)
April 2000                                       Three (3)
October 2000                                     Three (3)
April 2001                                       Three (3)
October 2001                                     Three (3)
</TABLE>

<TABLE>
<CAPTION>
                   Block I Aircraft
                   ----------------
<S>                                              <C>
January 2002                                     Four (4)
March 2002                                       Four (4)
April 2002                                       Two (2)
July 2002                                        Four (4)
October 2002                                     Four (4)
</TABLE>

<TABLE>
<CAPTION>
                   Block J Aircraft
                   ----------------
<S>                                              <C>
January 2003                                     Four (4)
March 2003                                       One (1)
</TABLE>

<TABLE>
<CAPTION>
                   Block K Aircraft
                   ----------------
<S>                                              <C>
April 2004                                       Two (2)
July 2004                                        Three (3)
</TABLE>

<TABLE>
<CAPTION>
                   Block L Aircraft
                   ----------------
<S>                                              <C>
October 1999                                     One (1)
November 1999                                    Two (2)
December 1999                                    One (1)
June 2000                                        Three (3)
July 2000                                        One (1)
August 2000                                      Two (2)
September 2000                                   One (1)
October 2000                                     One (1)
November 2000                                    Three (3)
December 2000                                    Two (2)
January 2001                                     One (1)
February 2001                                    One (1)
July 2001                                        One (1)
September 2001                                   One (1)
October 2001                                     One (1)
September 2002                                   Three (3)
</TABLE>


P.A. No. 1810                         15-9
K/SWA


<PAGE>   48


         2.2 Notice of Target Delivery Date. Boeing will give Buyer notice of
the Target Delivery Date of the Aircraft approximately 30 days prior to the
scheduled month of delivery.

         2.3 Notice of Delivery Date. If Boeing gives Buyer at least 7 days'
notice of the delivery date of the Aircraft, and an Aircraft delivery is delayed
beyond such delivery date due to the responsibility of Buyer, Buyer will
reimburse Boeing for all costs incurred by Boeing as a result of such delay,
including amounts for storage, insurance, Taxes, preservation or protection of
the Aircraft and interest on payments due.

         2.4 Place of Delivery. The Aircraft will be delivered at an airport
facility selected by Boeing in the State of Washington, unless mutually agreed
otherwise.

         2.5 Title and Risk of Loss. Title to and risk of loss of an Aircraft
will pass from Boeing to Buyer upon delivery of such Aircraft, but not prior
thereto.

         2.6 Bill of Sale. Upon delivery of an Aircraft Boeing will deliver to
Buyer a bill of sale conveying good title to such Aircraft, free of all liens,
claims, charges and encumbrances of every kind whatsoever, and such other
appropriate documents of title as Buyer may reasonably request.


P.A. No. 1810                         15-10
K/SWA


<PAGE>   49


ARTICLE 3. Price of Aircraft.

         3.1 Definitions.

                  3.1.1 Special Features are the features incorporated in
Exhibit A which have been selected by Buyer.

                  3.1.2 Base Aircraft Price is the Aircraft Basic Price
excluding the price of Special Features.

                  3.1.3 Aircraft Basic Price is comprised of the Base Aircraft
Price and the price of the Special Features.

                  3.1.4 Economic Price Adjustment is the adjustment to the
Aircraft Basic Price (Base Aircraft and Special Features) as calculated pursuant
to Exhibit D.

                  3.1.5 Aircraft Price is the total amount Buyer is to pay for
the Aircraft at the time of delivery.

         3.2 Aircraft Basic Price.

                  The Aircraft Basic Price, expressed in July 1992 dollars, is
set forth below:

<TABLE>
<CAPTION>
                     Base               Special        Aircraft
                     Aircraft Price     Features       Basic Price
<S>                  <C>                <C>            <C>
Block A, B, C,
D & E Aircraft       $ ***              $ ***          $ ***
Block F & G
Aircraft             $ ***              $ ***          $ ***
Block H
Aircraft             $ ***              $ ***          $ ***
Block I
Aircraft             $ ***              $ ***          $ ***
Block J
Aircraft             $ ***              $ ***          $ ***
Block K
Aircraft             $ ***              $ ***          $ ***
Block L Aircraft
                     $ ***              $ ***          $ ***
</TABLE>



         3.3 Aircraft Price. The Aircraft Price will be established at the time
of delivery of such Aircraft to Buyer and will be the sum of:

                  3.3.1 the Aircraft Basic Price, which is *** for the Block A,
B, C, D and E Aircraft, *** for the Block F and G Aircraft, *** for the Block H
Aircraft, *** for the


P.A. No. 1810                         15-11
K/SWA


<PAGE>   50


Block I Aircraft, *** for the Block J Aircraft, *** for the Block K Aircraft and
*** for the Block L Aircraft; plus

                  3.3.2 the Economic Price Adjustments for the Aircraft Basic
Price, as calculated pursuant to the formulas set forth in Exhibit D (Price
Adjustments Due to Economic Fluctuations - Aircraft); plus 3.3.3 other price
adjustments made pursuant to this Agreement or other written agreements executed
by Boeing and Buyer.

         3.4 Advance Payment Base Price.

                  3.4.1 Advance Payment Base Price. For advance payment
purposes, the following estimated delivery prices of the Aircraft (Advance
Payment Base Price) have been established, using currently available forecasts
of the escalation factors used by Boeing as of the date of signing this
Agreement. The Advance Payment Base Price of each Aircraft is set forth below:

<TABLE>
<CAPTION>
Month and Year of                                Advance Payment Base
Scheduled Delivery                               Price per Aircraft
------------------                               ------------------

                         Block A Aircraft ***
                         ----------------
<S>                                              <C>
October 1997
November 1997
</TABLE>

<TABLE>
<CAPTION>
                         Block B Aircraft ***
                         ----------------
<S>                                              <C>
January 1998
February 1998
March 1998
April 1998
May 1998
June 1998
July 1998
September 1998
</TABLE>

<TABLE>
<CAPTION>
                         Block C Aircraft ***
                         ----------------
<S>                                              <C>
February 1999
May 1999
July 1999
August 1999
September 1999
</TABLE>

<TABLE>
<CAPTION>
                         Block D Aircraft ***
                         ----------------
<S>                                              <C>
November 1999
December 1999
January 2000
March 2000
July 2000
September 2000
</TABLE>


P.A. No. 1810                         15-12
K/SWA


<PAGE>   51


<TABLE>
<CAPTION>
            Block E Aircraft ***
            ----------------
<S>                                              <C>
January 2001
March 2001
July 2001
September 2001
</TABLE>

<TABLE>
<CAPTION>
            Block F Aircraft ***
            ----------------
<S>                                              <C>
October 1998
November 1998
December 1998
</TABLE>

<TABLE>
<CAPTION>
            Block G Aircraft ***
            ----------------
<S>                                              <C>
March 1999
</TABLE>

<TABLE>
<CAPTION>
            Block H Aircraft ***
            ----------------
<S>                                              <C>
June 1999
July 1999
August 1999
September 1999
October 1999
April 2000
October 2000
April 2001
October 2001
</TABLE>

<TABLE>
<CAPTION>
            Block I Aircraft ***
            ----------------
<S>                                              <C>
January 2002
March 2002
April 2002
July 2002
October 2002
</TABLE>

<TABLE>
<CAPTION>
            Block J Aircraft ***
            ----------------
<S>                                              <C>
January 2003
March 2003
</TABLE>

<TABLE>
<CAPTION>
            Block K Aircraft ***
            ----------------
<S>                                              <C>
April 2004
July 2004
</TABLE>


P.A. No. 1810                         15-13
K/SWA


<PAGE>   52


<TABLE>
<CAPTION>
            Block L Aircraft ***
            ----------------
<S>                                              <C>
October 1999
November 1999
December 1999
June 2000
July 2000
August 2000
September 2000
October 2000
November 2000
December 2000
January 2001
February 2001
July 2001
September 2001
October 2001
September 2002
</TABLE>

                  3.4.2 Adjustment of Advance Payment Base Prices - Long-Lead
Aircraft. For Aircraft scheduled for delivery 36 months or more after the date
of this Agreement, the Advance Payment Base Prices appearing in Article 3.4.1
will be used to determine the amount of the first advance payment to be made by
Buyer on the Aircraft. No later than 25 months before the scheduled month of
delivery of each affected Aircraft, Boeing will increase or decrease the Advance
Payment Base Price of such Aircraft as required to reflect the effects of (i)
any adjustments in the Aircraft Basic Price pursuant to this Agreement and (ii)
the then-current forecasted escalation factors used by Boeing. Boeing will
provide the adjusted Advance Payment Base Prices for each affected Aircraft to
Buyer, and the advance payment schedule will be considered amended to substitute
such adjusted Advance Payment Base Prices.


P.A. No. 1810                         15-14
K/SWA


<PAGE>   53


6-1162-RLL-933R8


Southwest Airlines Co.
P.O. Box 36611 - Love Field
Dallas, Texas  75235

Subject:  Letter Agreement No. 6-1162-RLL-933R8 to
          Purchase Agreement No. 1810 -
          Option Aircraft


This Letter Agreement amends Purchase Agreement No. 1810 dated as of January 19,
1994 (the Agreement) between The Boeing Company (Boeing) and Southwest Airlines
Co. (Buyer) relating to Model 737-7H4 aircraft (Aircraft).

All terms used and not defined herein will have the same meaning as in the
Agreement.

In consideration of the purchase by Buyer of the Aircraft, Boeing hereby agrees
to manufacture and sell to Buyer sixty-two (62) additional Model 737-7H4
aircraft as described in paragraph 1 of Attachment A hereto (Option Aircraft)
and forty-six (46) Model 737-7H4 Rollover Option Aircraft (Rollover Option
Aircraft), subject to the terms and conditions set forth below.

1.       Delivery of Option Aircraft.

         The Option Aircraft will be delivered to Buyer during or before the
months set forth in the following schedule:









--------------------------------------------------------------------------------
***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   54


Southwest Airlines Co.
6-1162-RLL-933R8    Page 2


<TABLE>
<CAPTION>
                     Number of                Option
Month and Year       Option                  Aircraft
of Delivery          Aircraft                  Block
--------------       --------                --------
<S>                  <C>                      <C>
March 2003           Three  (3)                  M
April 2003           Two   (2)                   M
July 2003            Four  (4)                   M
October 2003         Four  (4)                   M

January 2004         Four (4)                    N
March 2004           One (1)                     N
April 2004           One   (1)                   N
August 2004          Two   (2)                   N
September 2004       Three (3)                   N
October 2004         Two   (2)                   N
</TABLE>

<TABLE>
<CAPTION>
                     Number of                Option
Month and Year       Option                  Aircraft
of Delivery          Aircraft                  Block
--------------       --------                --------
<S>                  <C>                     <C>
January 2005         Four (4)                    O
March 2005           Four (4)                    O
April 2005           Two (2)                     O
July 2005            Four (4)                    O
October 2005         Four (4)                    O

January 2006         Four (4)                    P
March 2006           Four (4)                    P
April 2006           Two (2)                     P
July 2006            Four (4)                    P
October 2006         Four (4)                    P
</TABLE>


2.       Delivery of Rollover Option Aircraft.

         2.1 The Rollover Option Aircraft will be delivered to Buyer during or
before the years set forth in the following schedule:

<TABLE>
<CAPTION>
                                     Option
Year of     Number of               Aircraft
Delivery    Option Aircraft           Block
--------    ---------------         --------
<S>         <C>                     <C>
2007        Twenty (20)                Q
2008        Twenty (20)                R
2009        Six (6)                    S
</TABLE>

         2.2 The forty-six (46) Rollover Option Aircraft are offered to Buyer
subject to the following conditions:


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   55


Southwest Airlines Co.
6-1162-RLL-933R8    Page 3


                  2.2.1 Buyer can exercise any forty-six (46) of the sixty-two
(62) Option Aircraft, and will be offered a Rollover Option Aircraft for each
option aircraft exercised up to and including forty-six (46).

                  2.2.2 Conversely to Article 2.2.1 above, if Buyer does not
exercise a minimum of forty-six (46) Option Aircraft, one Rollover Option
Aircraft will be deleted for each Option Aircraft not exercised by Buyer.

                  2.2.3 When Buyer exercises one or more Option Aircraft, Boeing
will offer the same quantity of Rollover Option Aircraft to Buyer in the years
identified in Article 2.1 above.

                  2.2.4 The Rollover Option Aircraft delivery month offered by
Boeing to Buyer will be at least 24 months from the Option exercise date of the
corresponding option.

                  2.2.5 When Boeing offers the Rollover Option Aircraft to
Buyer, Buyer will accept such Rollover Option Aircraft by wire transferring
$100,000 to Boeing. In the event Buyer exercises its option to purchase the
Rollover Option Aircraft, such application will be in accordance with Article
4.1 herein.

3.       Price.

         3.1 The advance payment base prices of the Option Aircraft set forth
below and in paragraph 2.1 of Attachment A represent the estimated delivery
prices of the Option Aircraft. The Option Aircraft pricing elements and
associated pricing terms and conditions are given in Attachment A.

         3.2 Price and escalation provisions for Model 737-7H4 aircraft
delivering after 2002, are not currently available. The estimated Advance
Payment Base Prices shown in paragraph 3.3 below and in paragraph 2.1 of
Attachment A are based on currently available price and escalation provisions.
As price and escalation provisions become available for Model 737-7H4 aircraft
delivering after 2002, such price and escalation provisions will be
appropriately applied to the applicable Option Aircraft.

For additional information relating to price and escalation provisions
applicable to Option Aircraft delivering after 2002 refer to paragraphs 2.2 and
3.2 of Attachment A.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   56


Southwest Airlines Co.
6-1162-RLL-933R8    Page 4

         3.3 The Advance Payment Base Prices of the Option Aircraft indicated
below do include an amount for special features in addition to those
specifically described in Attachment A but do not include any amount for items
of Buyer Furnished Equipment (BFE). An estimate for typical special features is
$ *** per Aircraft (expressed in 1992 STE dollars) and for BFE is $ *** per
Aircraft (expressed in delivery year dollars).

<TABLE>
<CAPTION>
Month and Year                   Advance Payment Base
of Delivery                   Price per Option Aircraft
-----------                   -------------------------

            Block M Aircraft
            ----------------
<S>                           <C>
March 2003                             ***
April 2003                             ***
July 2003                              ***
October 2003                           ***
</TABLE>

<TABLE>
<CAPTION>
            Block N Aircraft
            ----------------
<S>                           <C>
January 2004                           ***
March 2004                             ***
April 2004                             ***
August 2004                            ***
September 2004                         ***
October 2004                           ***
</TABLE>

<TABLE>
<CAPTION>
            Block O Aircraft
            ----------------
<S>                           <C>
January 2005                           ***
March 2005                             ***
April 2005                             ***
July 2005                              ***
October 2005                           ***
</TABLE>

<TABLE>
<CAPTION>
            Block P Aircraft
            ----------------
<S>                           <C>
January 2006                           ***
March 2006                             ***
April 2006                             ***
July 2006                              ***
October 2006                           ***
</TABLE>


         3.4 The Option Aircraft purchase price will be the applicable basic
price thereof at the time of Option Aircraft delivery adjusted in accordance
with Boeing's Aircraft escalation provisions contained in the definitive
agreement to purchase the Option Aircraft. The purchase price will include the
price for Seller Purchased Equipment (SPE) if Buyer has elected to change Buyer
Furnished Equipment (BFE) to SPE.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   57


Southwest Airlines Co.
6-1162-RLL-933R8    Page 5


4.       Option Aircraft Payment.

         4.1 In consideration of the granting of the option as set forth herein,
on or before the date Boeing and Buyer enter into a definitive agreement to
purchase the Aircraft, Buyer will pay a deposit to Boeing of $100,000 for each
Option Aircraft (Deposit). In the event Buyer exercises its option herein, the
amount of the Deposit will be credited against the first advance payment due for
such Option Aircraft pursuant to the advance payment schedule set forth in
paragraph 3 of Attachment A. The Deposits for the Option Aircraft will be
refunded to Buyer, without interest, if the parties do not enter into a
definitive Agreement for the Aircraft.

In the event that, after the parties enter into a definitive agreement to
purchase the Aircraft, Buyer does not exercise its option to purchase the Option
Aircraft pursuant to the terms and conditions set forth herein, Boeing will be
entitled to retain the Deposits for the Option Aircraft except as provided in
paragraphs 6 herein.

         4.2 Advance payments in the amount of 30% of the advance payment base
price will be payable on the Option Aircraft in accordance with paragraph 3 of
Attachment A. The remainder of the Option Aircraft purchase price is due at the
time of delivery of the Option Aircraft.

5.       Option Exercise.

         5.1 To exercise its Option, Buyer will give written or telegraphic
notice thereof to Boeing on or before eighteen (18) months prior to the first
day of the delivery month of each Option Aircraft.

In such notice Buyer will select the Option Model type, and the applicable
delivery positions.

         5.2 It is understood and agreed that Boeing may accelerate the option
exercise dates specified above if Boeing must make production decisions which
are dependent on Buyer's decision to buy the Option Aircraft. If Boeing elects
to accelerate the option exercise dates, Boeing will do so by giving written or
telegraphic notice thereof to Buyer. Such notice will specify the revised option
exercise dates, which will not be earlier than 30 days after the date of


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   58


Southwest Airlines Co.
6-1162-RLL-933R8    Page 6


transmittal of such notice, and the Option Aircraft delivery positions affected
by such revision. If Buyer fails to exercise its option for any Option Aircraft
affected by such revised dates, the Deposit applicable to such Option Aircraft
will be promptly refunded, with interest, to Buyer. The interest rate for
calculation of the interest associated with such refund is the rate of two
percent (2%) below the Citibank base rate in effect from time to time during the
period the option deposit is held by Boeing.

6.       Contract Terms.

         It is understood that Boeing and Buyer will use their best efforts to
enter into a definitive agreement for the Option Aircraft within thirty (30)
days after Buyer exercises an option to purchase Option Aircraft pursuant to
paragraph 5 covering the detailed terms and conditions for the sale of such
Option Aircraft.

Such definitive agreement will include the terms and conditions contained herein
together with the terms and conditions, not inconsistent herewith, contained in
Boeing's then-current standard form of purchase agreement for the sale of Model
737-700 aircraft in effect as of the date of option exercise and such additional
terms and conditions as may be mutually agreed upon. In the event the parties
have not entered into such an agreement within the time period contemplated
herein, either party may, exercisable by written or telegraphic notice given to
the other within thirty (30) days after such period, terminate the purchase of
such Option Aircraft.

7.       Termination of Option to Purchase.

         Either Boeing or Buyer may terminate the option to purchase an Option
Aircraft if any of the following events are not accomplished by the respective
dates contemplated in this letter agreement, or in the Agreement, as the case
may be:

         (i) termination of the purchase of the Aircraft under the Agreement for
any reason;

         (ii) payment by Buyer of the Deposit with respect to an Option Aircraft
pursuant to paragraph 4.1 herein;

         (iii) exercise of an option to purchase an Option Aircraft pursuant to
the terms hereof. Any termination of an option to purchase by Boeing which is
based on the termination of the purchase of


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   59


Southwest Airlines Co.
6-1162-RLL-933R8    Page 7


Aircraft under the Agreement will be on a one-for-one basis, for each Aircraft
so terminated.

Any cancellation of an option to purchase which is based on failure to make the
required Deposit or to exercise the option to purchase shall only apply to the
Option Aircraft so canceled.

Termination of an option to purchase provided by this letter agreement will be
caused by either party giving written notice to the other within 10 days after
the applicable date. Upon receipt of such notice, all rights and obligations of
the parties with respect to an Option Aircraft for which the option to purchase
has been terminate will thereupon terminate.

If termination is result of a revision of an option exercise date by Boeing
pursuant to paragraph 5.2, Boeing will promptly refund to Buyer, without
interest, any payments received from Buyer, including the Deposit, with respect
to the Option Aircraft for which the option is terminated. If termination is for
any other reason, Boeing will promptly refund to Buyer, without interest, any
payments received from Buyer with respect to the affected Option Aircraft,
except the Deposit, which Buyer may apply to any model Boeing aircraft purchased
by Buyer from Boeing at a future date.

8. Confidential Treatment. Buyer understands that certain commercial and
financial information contained in this Letter Agreement including any
attachments hereto is considered by Boeing as confidential. Buyer agrees that it
will treat this Letter Agreement and the


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   60


Southwest Airlines Co.
6-1162-RLL-933R8    Page 8


information contained herein as confidential and will not, without the prior
written consent of Boeing, disclose this Letter Agreement or any information
contained herein to any other person or entity except as provided in Letter
Agreement No. 6-1162-RLL-934R1.

Very truly yours,

THE BOEING COMPANY



By  /S/ DAWN S. FOSTER
  --------------------------

Its ATTORNEY-IN-FACT
    ------------------------

ACCEPTED AND AGREED TO this

date: April 29, 1999

SOUTHWEST AIRLINES CO.


By  /S/ LAURA WRIGHT
  --------------------------
Its  TREASURER
    ------------------------
Attachments


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   61


Attachment A to
6-1162-RLL-933R8
Page 1


Model 737-7H4 Aircraft

1.       Option Aircraft Description and Changes.

         1.1 Aircraft Description. The Option Aircraft is described by Boeing
Detail Specification D6-38808-1, Dated October 30 ,1996.

         1.2 Changes. The Detail Specification will be revised to include:

                  (1) Changes applicable to the basic Model 737-700 aircraft
which are developed by Boeing between the date of the Detail Specification and
the signing of a definitive agreement to purchase the Option Aircraft.

                  (2) Changes mutually agreed upon.

                  (3) Changes required to obtain a Standard Certificate of
Airworthiness.

                  (4) To provide sufficient Option Aircraft manufacturing and
procurement lead time it is necessary for Boeing and Buyer to reach final
agreement on the Option Aircraft configuration, including BFE/SPE vendor
selection fifteen (15) months prior to delivery of each Option Aircraft. If such
items are not resolved by the indicated dates, Boeing reserves the right to
amend this letter agreement:

                           (i) to adjust the scheduled delivery of the Option
Aircraft to a later time period and,

                           (ii) to make such other changes as are appropriate
and consistent with the revised Option Aircraft deliveries.

         1.3 Effect of Changes. Changes to the Detail Specification incorporated
pursuant to the provisions of the clauses above will include the effects of such
changes upon Option Aircraft weight, balance, design and performance.
Performance guarantees for the Option Aircraft which are mutually acceptable to
the parties will be included in the definitive agreement for the Option
Aircraft.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   62


Attachment A to
6-1162-RLL-933
Page 2



P.A. No. 1810
K/SWA


2.       Price Description

         2.1      Price Elements Per Aircraft


<TABLE>
<CAPTION>
                     1                2         3
                     -                -         -

                 AIRCRAFT &                             ADV. PMT.
AIRCRAFT       ESTIMATED SPECIAL             ESTIMATED  BASE PRICE
DELIVERY        FEATURES PRICE    ESTIMATED  ESCALATION (Elements)
MO. & YR.       (JULY 1992$)     ESCALATION  SHARING     1 + 2 + 3
---------       ---------------- ----------  ---------- -----------
<S>            <C>               <C>         <C>        <C>
BLOCK M
-------

March 2003      $    ***            ***        ***         ***
April 2003      $    ***            ***        ***         ***
July 2003       $    ***            ***        ***         ***
October 2003    $    ***            ***        ***         ***

BLOCK N
-------

January 2004    $    ***            ***        ***         ***
March 2004      $    ***            ***        ***         ***
April 2004      $    ***            ***        ***         ***
August 2004     $    ***            ***        ***         ***
September 2004  $    ***            ***        ***         ***
October 2004    $    ***            ***        ***         ***

BLOCK O
-------

January 2005    $    ***            ***        ***         ***
March 2005      $    ***            ***        ***         ***
April 2005      $    ***            ***        ***         ***
July 2005       $    ***            ***        ***         ***
October 2005    $    ***            ***        ***         ***

BLOCK P
-------

January 2006    $    ***            ***        ***         ***
March 2006      $    ***            ***        ***         ***
April 2006      $    ***            ***        ***         ***
July 2006       $    ***            ***        ***         ***
October 2006    $    ***            ***        ***         ***
</TABLE>


Continued Next Page...


P.A. No. 1810
K/SWA                                                                 SA-9


<PAGE>   63


Attachment A to
6-1162-RLL-933R8
Page 3


2.       Price Description. (Continued)

         2.2 Price Adjustments For Option Aircraft Delivering From March 2003
through December 2009.

         2.2.1 Special Features. The price for Special Features incorporated in
the Option Aircraft Detail Specification will be adjusted to Boeing's
then-current prices for such features as of the date of execution of the
definitive agreement for the Option Aircraft.

         2.2.2 Escalation Adjustments. For escalation provisions applicable to
Option Aircraft delivering after 2002, see paragraph 2.2.6 below.

         2.2.3 Base Price Adjustments for FAA Changes. The Aircraft Basic Price
of the Option Aircraft will be adjusted for any FAA mandated changes
incorporated into the Aircraft.

         2.2.4 Price Adjustments for Changes. Boeing may adjust the Aircraft
Basic Price and the Advance Payment Base Price for any changes mutually agreed
upon subsequent to the date that Buyer and Boeing enter into a definitive
agreement for the Option Aircraft.

         2.2.5 Base Price Adjustments. The Aircraft Basic Price of the Option
Aircraft will be adjusted to Boeing's then-current prices as of the date of
execution of the definitive agreement for the Option Aircraft in accordance with
the agreement reached below. The Aircraft Basic Price starting point for options
delivering in 2003 is $ *** (July 1992 STE), for options delivering in 2004 is $
*** (July 1992 STE), for options delivering in 2005 through 2009 is $ *** (July
1992 STE). Such Aircraft Basic Price may increase in accordance with paragraphs
2.2.1, 2.2.2, 2.2.3 and 2.2.4. For any other changes to the Aircraft Basic
Price, Boeing may increase the Aircraft Basic Price by a maximum of $ *** (July
1992 STE) for Aircraft delivering in 2005 and by a maximum of $ *** (July 1992
STE) per year or portion thereof starting in January 2006.

         2.2.6 Prices for Long Lead Time Aircraft. Boeing has not established
escalation provisions for Model 737-700 aircraft for delivery 2003 and after.
Such escalation provisions (i) will be incorporated into the Option Aircraft
definitive agreement when such information is available and (ii) will be the
then-current escalation provisions applicable to the same model aircraft and
engines delivering in the same time period as the Option Aircraft. The resulting
revisions to the definitive agreement will


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   64


Attachment A to
6-1162-RLL-933R8
Page 4


include but not be limited to, adjustment of the Aircraft Basic Price of the
Option Aircraft, the Advance Payment Base Price, the Aircraft escalation
provisions and the advance payment amounts due on the Option Aircraft.

         2.2.7 BFE to SPE. An estimate of the total price for items of Buyer
Furnished Equipment (BFE) changed to Seller Purchased Equipment (SPE) pursuant
to the Configuration Specification is included in the Option Aircraft price
build-up. The purchase price of the Option Aircraft will be adjusted by the
price charged to Boeing for such items plus 10% of such price. If all BFE except
developmental avionics is converted to SPE, Boeing will waive the 10% fee.

3.       Advance Payment Schedules, Prices and Adjustments.

         3.1 Buyer will pay to Boeing advance payments for the Option Aircraft
on the dates and in the amounts determined below.


P.A. No. 1810
K/SWA                                                                       SA-9



<PAGE>   65


Attachment A to
6-1162-RLL-933R8
Page 5


<TABLE>
<CAPTION>
                                     Amount Due per Aircraft
                                       (Percentage times
Due Date of Payment                Advance Payment Base Price)
-------------------
<S>                                           <C>
Deposit                                        $100,000 (if applicable)

18 months prior to the first                   15% (less the
day of the scheduled delivery                       Deposit if any)
month of the Aircraft

12 months prior to the first                    5%
day of the scheduled delivery
month of the Aircraft

9 months prior to the first                     5%
day of the scheduled delivery
month of the Aircraft

6 months prior to the first                     5%
day of the scheduled delivery
month of the Aircraft
                                              ---

           Total                               30%
</TABLE>

Any advance payments that would be past due as of the date of signing the
definitive purchase agreement for the Option Aircraft in accordance with the
above schedule are due and payable on such date.

         3.2 Option Aircraft advance payment base prices will be increased or
decreased, as appropriate, at the time of signing of the definitive purchase
agreement for the Option Aircraft, using the then-current forecasted aircraft
escalation factors used by Boeing, to determine the amount of the advance
payments to be made by Buyer on the Option Aircraft.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   66


Attachment B to
6-1162-RLL-933R8
Page 1


                             PRICE ADJUSTMENT DUE TO
                              ECONOMIC FLUCTUATIONS
                            AIRCRAFT PRICE ADJUSTMENT
                             (July 1992 Base Price)


1.       Formula.

         The Aircraft Price Adjustment will be determined at the time of
Aircraft delivery in accordance with the following formula:

        Pa = (P)(L + M - 1)

         Where:

        Pa = Aircraft Price Adjustment.

         L =      .65 x  ECI
                        -----
                        116.2

         M =      .35 x  ICI
                        -----
                        115.9

         P = Aircraft Basic Price (as set forth in
             Article 3.2 of this Agreement).

       ECI = A value using the "Employment Cost Index for workers in
             aerospace manufacturing" (aircraft manufacturing, standard
             industrial classification code 3721, compensation, base month
             and year June 1989 = 100), as released by the Bureau of Labor
             Statistics, U.S. Department of Labor on a quarterly basis for
             the months of March, June, September and December, calculated
             as follows: A three-month arithmetic average value (expressed
             as a decimal and rounded to the nearest tenth) will be
             determined using the months set forth in the table below for
             the applicable Aircraft, with the released Employment Cost
             Index value described above for the month of March also being
             used for the months of January and February; the value for
             June also used for April and May; the value for September also
             used for July and August; and the value for December also used
             for October and November.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   67


Attachment B to
6-1162-RLL-933R8
Page 3


2. If at the time of delivery of an Aircraft Boeing is unable to determine the
Aircraft Price Adjustment because the applicable values to be used to determine
the ECI and ICI have not been released by the Bureau of Labor Statistics, then:

         2.1 The Aircraft Price Adjustment, to be used at the time of delivery
of each of the Aircraft, will be determined by utilizing the escalation
provisions set forth above. The values released by the Bureau of Labor
Statistics and available to Boeing 30 days prior to scheduled Aircraft delivery
will be used to determine the ECI and ICI values for the applicable months
(including those noted as preliminary by the Bureau of Labor Statistics) to
calculate the Aircraft Price Adjustment. If no values have been released for an
applicable month, the provisions set forth in Paragraph 2.2 below will apply. If
prior to delivery of an Aircraft the U.S. Department of Labor changes the base
year for determination of the ECI or ICI values as defined above, such rebased
values will be incorporated in the Aircraft Price Adjustment calculation. The
payment by Buyer to Boeing of the amount of the Purchase Price for such
Aircraft, as determined at the time of Aircraft delivery, will be deemed to be
the payment for such Aircraft required at the delivery thereof.

         2.2 If prior to delivery of an Aircraft the U.S. Department of Labor
substantially revises the methodology used for the determination of the values
to be used to determine the ECI and ICI values (in contrast to benchmark
adjustments or other corrections of previously released values), or for any
reason has not released values needed to determine the applicable Aircraft Price
Adjustment, the parties will, prior to delivery of any such Aircraft, select a
substitute for such values from data published by the Bureau of Labor Statistics
or other similar data reported by non-governmental United States organizations,
such substitute to lead in application to the same adjustment result, insofar as
possible, as would have been achieved by continuing the use of the original
values as they may have fluctuated during the applicable time period.
Appropriate revision of the formula will be made as required to reflect any
substitute values. However, if within 24 months from delivery of the Aircraft
the Bureau of Labor Statistics should resume releasing values for the months
needed to determine the Aircraft Price Adjustment, such values will be used to
determine any increase or decrease in the Aircraft Price Adjustment for the
Aircraft from that determined at the time of delivery of such Aircraft.


P.A. No. 1810
K/SWA                                                                       SA-9


<PAGE>   68


Attachment B to
6-1162-RLL-933R8
Page 4


         2.3 In the event escalation provisions are made non-enforceable or
otherwise rendered null and void by any agency of the United States Government,
the parties agree, to the extent they may lawfully do so, to equitably adjust
the Purchase Price of any affected Aircraft to reflect an allowance for
increases or decreases in labor compensation and material costs occurring since
February, 1992, which is consistent with the applicable provisions of paragraph
1 of this Exhibit D.

3. For the calculations herein, the values released by the Bureau of Labor
Statistics and available to Boeing 30 days prior to scheduled Aircraft delivery
will be used to determine the ECI and ICI values for the applicable months
(including those noted as preliminary by the Bureau of Labor Statistics) to
calculate the Aircraft Price Adjustment.

Note:    Any rounding of a number, as required under this Exhibit D with respect
         to escalation of the airframe price, will be accomplished as follows:
         if the first digit of the portion to be dropped from the number to be
         rounded is five or greater, the preceding digit will be raised to the
         next higher number.

<PAGE>   69

                                                                    EXHIBIT 10.1

                          Supplemental Agreement No. 10

                                       to

                           Purchase Agreement No. 1810

                                     between

                               The Boeing Company

                                       and

                             SOUTHWEST AIRLINES CO.

                    Relating to Boeing Model 737-7H4 Aircraft


         THIS SUPPLEMENTAL AGREEMENT, entered into as of August 2, 1999, by and
between THE BOEING COMPANY, a Delaware corporation with its principal offices in
Seattle, Washington, (Boeing) and SOUTHWEST AIRLINES CO., a Texas corporation
with its principal offices in City of Dallas, State of Texas (Buyer);

         WHEREAS, the parties hereto entered into Purchase Agreement No. 1810
dated January 19, 1994, relating to Boeing Model 737-7H4 aircraft (the
Agreement) and;

         WHEREAS, Buyer has agreed to accelerate one Block H Aircraft from April
2000 to March 2000;

         NOW THEREFORE, in consideration of the mutual covenants herein
contained, the parties agree to amend the Agreement as follows:


--------------------------------------------------------------------------------
***      PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
         OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND EXCHANGE
         COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT APPLICATION FILED WITH
         THE COMMISSION.


P.A. No. 1810                        SA-10-1
K/SWA

<PAGE>   70



1. The Table of Contents of the Agreement is deleted in its entirety and a new
Table of Contents is attached hereto and incorporated into the Agreement by this
reference.

2. Article 2, entitled "Delivery, Title and Risk of Loss," paragraph 2.1,
entitled "Time of Delivery," is deleted in its entirety and replaced by a new
paragraph 2.1 revised to add one (1) Block H Aircraft delivering in March 2000
and to change the quantity of Block H Aircraft delivering in April 2000 from
three (3) to two (2). Such new pages 2-1, 2-2 and 2-3 are attached hereto and
incorporated into the Agreement by this reference.

3. Article 3, entitled "Price of Aircraft", paragraph 3.4 entitled "Advance
Payment Base Price," subparagraph 3.4.1 entitled "Advance Payment Base Price" is
revised by adding an Advance Payment Base Price for the Block H Aircraft
delivering in March 2000. Such new pages 3-1, 3-2, 3-3 and 3-4 are attached
hereto and incorporated into the Agreement by this reference.

4. All references in the Letter Agreements associated with Purchase Agreement
No. 1810 shall be deemed to refer to the purchase by Buyer of one hundred
forty-two (142) Model 737-7H4 Aircraft, sixty-two (62) Model 737-7H4 Option
Aircraft and forty-six (46) Model 737-7H4 Rollover Option Aircraft, to the
extent such reference is not specifically addressed herein.

5. Within three (3) business days of execution of this Supplemental Agreement,
Boeing will refund to Buyer ***. Such amount reflects the difference in advance
payments due as a result of the acceleration of one (1) Block H Aircraft from
April 2000 to March 2000.

The Agreement will be deemed to be supplemented to the extent herein provided
and as so supplemented will continue in full force and effect.


P.A. No. 1810                        SA-10-2
K/SWA

<PAGE>   71




EXECUTED IN DUPLICATE as of the day and year first above written.

THE BOEING COMPANY                  SOUTHWEST AIRLINES CO.



By:    /s/ DAWN S. FOSTER           By:  /s/ LAURA WRIGHT
    ------------------------           ------------------

Its:    ATTORNEY-IN-FACT            ITS:   TREASURER
     -----------------------            -----------------


P.A. No. 1810                        SA-10-3
K/SWA


<PAGE>   72


                               PURCHASE AGREEMENT

                                     between

                               THE BOEING COMPANY

                                       and

                             SOUTHWEST AIRLINES CO.






                    Relating to Boeing Model 737-7H4 Aircraft

                         Purchase Agreement Number 1810













--------------------------------------------------------------------------------
***          PURSUANT TO 17 CFR, 240.246-2, CONFIDENTIAL INFORMATION HAS BEEN
             OMITTED AND HAS BEEN FILED SEPARATELY WITH THE SECURITIES AND
             EXCHANGE COMMISSION PURSUANT TO A CONFIDENTIAL TREATMENT
             APPLICATION FILED WITH THE COMMISSION.



P.A. No. 1810                         15-1
K/SWA

<PAGE>   73



                                TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                       Page            SA
                                                                       Number         Number
                                                                       ------         ------
<S>       <C>                                                          <C>            <C>
ARTICLES


1.        Subject Matter of Sale..........................................1-1          SA-9

2.        Delivery, Title and Risk
          of Loss.........................................................2-1         SA-10

3.        Price of Aircraft...............................................3-1         SA-10

4.        Taxes...........................................................4-1

5.        Payment.........................................................5-1

6.        Excusable Delay.................................................6-1

7.        Changes to the Detail
          Specification...................................................7-1          SA-1

8.        Federal Aviation Requirements and
          Certificates and Export License.................................8-1

9.        Representatives, Inspection,
          Flights and Test Data...........................................9-1

10.       Assignment, Resale or Lease....................................10-1

11.       Termination for Certain Events.................................11-1

12.       Product Assurance; Disclaimer and
          Release; Exclusion of Liabilities;
          Customer Support; Indemnification
          and Insurance..................................................12-1

13.       Buyer Furnished Equipment and
          Spare Parts....................................................13-1

14.       Contractual Notices and Requests...............................14-1

15.       Miscellaneous..................................................15-1
</TABLE>


P.A. No. 1810                         15-2
K/SWA

<PAGE>   74


                                TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                          SA
                                                      Number
                                                      ------
<S>          <C>                                      <C>

EXHIBITS
--------

A            Aircraft Configuration                     SA-1

B            Product Assurance Document                 SA-1

C            Customer Support Document

D            Price Adjustments Due to
             Economic Fluctuations - Aircraft

E            Buyer Furnished Equipment
             Provisions Document

F            Defined Terms Document



LETTER AGREEMENTS


1810-1       Waiver of Aircraft Demonstration Flight
</TABLE>




P.A. No. 1810                         15-3
K/SWA

<PAGE>   75



                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                      SA
                                                                  Number
                                                                  ------
<S>                   <C>                                         <C>
RESTRICTED LETTER AGREEMENTS
----------------------------

6-1162-RLL-932        Promotional Support

6-1162-RLL-933R8      Option Aircraft                             SA-9

6-1162-RLL-934R1      Disclosure of Confidential                  SA-1
                      Information

6-1162-RLL-935R1      Performance Guarantees                      SA-1

6-1162-RLL-936R4      Certain Contractual Matters                 SA-4

6-1162-RLL-937        Alternate Advance Payment Schedule

6-1162-RLL-938        ***

6-1162-RLL-939R1      Certification Flight Test Aircraft          SA-1

6-1162-RLL-940R1      Training Matters                            SA-1

6-1162-RLL-941R1      Other Matters                               SA-1

6-1162-RLL-942        Open Configuration Matters

6-1162-RLL-943R1      Substitution Rights                         SA-6

6-1162-RLL-944        Airframe Maintenance Material Cost
                      Protection Program

6-1162-RLL-945        Comparison of 737-7H4 and 737-3H4
                      Block Fuel Burn

6-1162-RLL-1855R3     Additional Contractual Matters              SA-4

6-1162-RLL-1856       ***                                         SA-1

6-1162-RLL-1857       Service Ready Validation Program            SA-1
                      Field Test

6-1162-RLL-1858R1     Escalation Matters                          SA-4
</TABLE>


P.A. No. 1810                         15-4
K/SWA

<PAGE>   76



                             TABLE OF CONTENTS CON'T

<TABLE>
<CAPTION>
                                                             SA
                                                         Number
                                                         ------
<S>               <C>                                    <C>
RESTRICTED LETTER AGREEMENTS
----------------------------

6-1162-RLL-2036   Amortization of Costs for
                  Customer Unique Changes                SA-1

6-1162-RLL-2037   Reconciliation of the Aircraft         SA-1
                  Basic Price

6-1162-RLL-2073   Maintenance Training Matters           SA-1
</TABLE>


P.A. No. 1810                         15-5
K/SWA

<PAGE>   77


                           PURCHASE AGREEMENT NO. 1810

                                   Relating to

                          BOEING MODEL 737-7H4 AIRCRAFT

                          ----------------------------


         This Agreement is entered into as of January 19th 1994, by and between
The Boeing Company, a Delaware corporation, with its principal office in
Seattle, Washington (Boeing), and Southwest Airlines Co., a Texas corporation,
with its principal office in the City of Dallas, State of Texas (Buyer).

Accordingly, Boeing and Buyer agree as follows:







P.A. No. 1810                         15-6
K/SWA

<PAGE>   78


ARTICLE 2.   Delivery, Title and Risk of Loss.

         2.1 Time of Delivery. The Aircraft will be delivered to Buyer by
Boeing, assembled and ready for flight and Buyer will accept delivery of the
Aircraft, in accordance with the following schedule:

<TABLE>
<CAPTION>
             Month and Year
               of Delivery                           Quantity of Aircraft
             --------------                          --------------------
<S>                             <C>                  <C>
                                Block A Aircraft
                                ----------------
             October 1997                                     Two (2)
             November 1997                                    Two (2)

                                Block B Aircraft
                                ----------------

             January 1998                                     Two (2)
             February 1998                                    Three (3)
             March 1998                                       Two (2)
             April 1998                                       Two (2)
             May 1998                                         Two (2)
             June 1998                                        One (1)
             July 1998                                        Two (2)
             September 1998                                   Two (2)

                                Block C Aircraft
                                ----------------

             February 1999                                    Four (4)
             May 1999                                         Four (4)
             July 1999                                        Four (4)
             August 1999                                      One (1)
             September 1999                                   Three (3)

                                Block D Aircraft
                                ----------------

             November 1999                                    Two (2)
             December 1999                                    One (1)
             January 2000                                     One (1)
             March 2000                                       Four (4)
             July 2000                                        Four (4)
             September 2000                                   Three (3)

                                Block E Aircraft
                                ----------------

             January 2001                                     Three (3)
             March 2001                                       Three (3)
             July 2001                                        Three (3)
             September 2001                                   Three (3)
</TABLE>

P.A. No. 1810                         15-7
K/SWA

<PAGE>   79




<TABLE>
<S>                             <C>                           <C>
                                Block F Aircraft
                                ----------------

             October 1998                                     One (1)
             November 1998                                    Two (2)
             December 1998                                    Two (2)

                                Block G Aircraft
                                ----------------

             March 1999                                       Two (2)

                                Block H Aircraft
                                ----------------

             June 1999                                        Two (2)
             July 1999                                        One (1)
             August 1999                                      One (1)
             September 1999                                   Two (2)
             October 1999                                     One (1)
             March 2000                                       One (1)
             April 2000                                       Two (2)
             October 2000                                     Three (3)
             April 2001                                       Three (3)
             October 2001                                     Three (3)

                                Block I Aircraft
                                ----------------

             January 2002                                     Four (4)
             March 2002                                       Four (4)
             April 2002                                       Two (2)
             July 2002                                        Four (4)
             October 2002                                     Four (4)

                                Block J Aircraft
                                ----------------

             January 2003                                     Four (4)
             March 2003                                       One (1)

                                Block K Aircraft
                                ----------------

             April 2004                                       Two (2)
             July 2004                                        Three (3)
</TABLE>

P.A. No. 1810                         15-8
K/SWA

<PAGE>   80




<TABLE>
<S>                             <C>                           <C>
                                Block L Aircraft
                                ----------------

             October 1999                                     One (1)
             November 1999                                    Two (2)
             December 1999                                    One (1)
             June 2000                                        Three (3)
             July 2000                                        One (1)
             August 2000                                      Two (2)
             September 2000                                   One (1)
             October 2000                                     One (1)
             November 2000                                    Three (3)
             December 2000                                    Two (2)
             January 2001                                     One (1)
             February 2001                                    One (1)
             July 2001                                        One (1)
             September 2001                                   One (1)
             October 2001                                     One (1)
             September 2002                                   Three (3)
</TABLE>


         2.2 Notice of Target Delivery Date. Boeing will give Buyer notice of
the Target Delivery Date of the Aircraft approximately 30 days prior to the
scheduled month of delivery.

         2.3 Notice of Delivery Date. If Boeing gives Buyer at least 7 days'
notice of the delivery date of the Aircraft, and an Aircraft delivery is delayed
beyond such delivery date due to the responsibility of Buyer, Buyer will
reimburse Boeing for all costs incurred by Boeing as a result of such delay,
including amounts for storage, insurance, Taxes, preservation or protection of
the Aircraft and interest on payments due.

         2.4 Place of Delivery. The Aircraft will be delivered at an airport
facility selected by Boeing in the State of Washington, unless mutually agreed
otherwise.

         2.5 Title and Risk of Loss. Title to and risk of loss of an Aircraft
will pass from Boeing to Buyer upon delivery of such Aircraft, but not prior
thereto.

         2.6 Bill of Sale. Upon delivery of an Aircraft Boeing will deliver to
Buyer a bill of sale conveying good title to such Aircraft, free of all liens,
claims, charges and encumbrances of every kind whatsoever, and such other
appropriate documents of title as Buyer may reasonably request.


P.A. No. 1810                         15-9
K/SWA

<PAGE>   81




ARTICLE 3.        Price of Aircraft.

         3.1      Definitions.

                  3.1.1 Special Features are the features incorporated in
Exhibit A which have been selected by Buyer.

                  3.1.2 Base Aircraft Price is the Aircraft Basic Price
excluding the price of Special Features.

                  3.1.3 Aircraft Basic Price is comprised of the Base Aircraft
Price and the price of the Special Features.

                  3.1.4 Economic Price Adjustment is the adjustment to the
Aircraft Basic Price (Base Aircraft and Special Features) as calculated pursuant
to Exhibit D.

                  3.1.5 Aircraft Price is the total amount Buyer is to pay for
the Aircraft at the time of delivery.

         3.2      Aircraft Basic Price.

                  The Aircraft Basic Price, expressed in July 1992 dollars, is
set forth below:

<TABLE>
<CAPTION>
                                 Base                            Special                            Aircraft
                                 Aircraft Price                  Features                           Basic Price
                                 --------------                  --------                           -----------
<S>                              <C>                             <C>                                <C>
Block A, B, C,
D & E Aircraft                   $***                            $***                               $***
Block F & G
Aircraft                         $***                            $***                               $***
Block H
Aircraft                         $***                            $***                               $***
Block I
Aircraft                         $***                            $***                               $***
Block J
Aircraft                         $***                            $***                               $***
Block K
Aircraft                         $***                            $***                               $***
Block L Aircraft
                                 $***                            $***                               $***
</TABLE>



         3.3      Aircraft Price. The Aircraft Price will be established at the
time of delivery of such Aircraft to Buyer and will be the sum of:

                  3.3.1 the Aircraft Basic Price, which is ($***) for the Block
A, B, C, D and E Aircraft, ($***) for the Block F and G Aircraft, ($***) for the
Block H Aircraft, ($***) for the Block I Aircraft, ($***) for the Block J


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<PAGE>   82


Aircraft, ($***) for the Block K Aircraft and ($***) for the Block L Aircraft;
plus

                  3.3.2 the Economic Price Adjustments for the Aircraft Basic
Price, as calculated pursuant to the formulas set forth in Exhibit D (Price
Adjustments Due to Economic Fluctuations - Aircraft); plus
                  3.3.3 other price adjustments made pursuant to this Agreement
or other written agreements executed by Boeing and Buyer.

         3.4      Advance Payment Base Price.

                  3.4.1 Advance Payment Base Price. For advance payment
purposes, the following estimated delivery prices of the Aircraft (Advance
Payment Base Price) have been established, using currently available forecasts
of the escalation factors used by Boeing as of the date of signing this
Agreement. The Advance Payment Base Price of each Aircraft is set forth below:

<TABLE>
<CAPTION>
             Month and Year of                                Advance Payment Base
             Scheduled Delivery                               Price per Aircraft
             ------------------                               --------------------
<S>                                     <C>                   <C>

                                        Block A Aircraft
                                        ----------------

             October 1997                                            $***
             November 1997                                           $***

                                        Block B Aircraft
                                        ----------------

             January 1998                                            $***
             February 1998                                           $***
             March 1998                                              $***
             April 1998                                              $***
             May 1998                                                $***
             June 1998                                               $***
             July 1998                                               $***
             September 1998                                          $***
</TABLE>


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<TABLE>
<S>                                     <C>                          <C>
                                        Block C Aircraft
                                        ----------------

             February 1999                                           $***
             May 1999                                                $***
             July 1999                                               $***
             August 1999                                             $***
             September 1999                                          $***

                                        Block D Aircraft
                                        ----------------

             November 1999                                           $***
             December 1999                                           $***
             January 2000                                            $***
             March 2000                                              $***
             July 2000                                               $***
             September 2000                                          $***

                                        Block E Aircraft
                                        ----------------

             January 2001                                            $***
             March 2001                                              $***
             July 2001                                               $***
             September 2001                                          $***

                                        Block F Aircraft
                                        ----------------

             October 1998                                            $***
             November 1998                                           $***
             December 1998                                           $***

                                        Block G Aircraft
                                        ----------------

             March 1999                                              $***

                                        Block H Aircraft
                                        ----------------

             June 1999                                               $***
             July 1999                                               $***
             August 1999                                             $***
             September 1999                                          $***
             October 1999                                            $***
             March 2000                                              $***
             April 2000                                              $***
             October 2000                                            $***
             April 2001                                              $***
             October 2001                                            $***
</TABLE>


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<TABLE>
<S>                             <C>                         <C>
                                Block I Aircraft
                                ----------------

             January 2002                                   $***
             March 2002                                     $***
             April 2002                                     $***
             July 2002                                      $***
             October 2002                                   $***

                                Block J Aircraft
                                ----------------

             January 2003                                   $***
             March 2003                                     $***

                                Block K Aircraft
                                ----------------

             April 2004                                     $***
             July 2004                                      $***

                                Block L Aircraft
                                ----------------

             October 1999                                   $***
             November 1999                                  $***
             December 1999                                  $***
             June 2000                                      $***
             July 2000                                      $***
             August 2000                                    $***
             September 2000                                 $***
             October 2000                                   $***
             November 2000                                  $***
             December 2000                                  $***
             January 2001                                   $***
             February 2001                                  $***
             July 2001                                      $***
             September 2001                                 $***
             October 2001                                   $***
             September 2002                                 $***
</TABLE>


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<PAGE>   85




                  3.4.2 Adjustment of Advance Payment Base Prices - Long-Lead
Aircraft. For Aircraft scheduled for delivery 36 months or more after the date
of this Agreement, the Advance Payment Base Prices appearing in Article 3.4.1
will be used to determine the amount of the first advance payment to be made by
Buyer on the Aircraft. No later than 25 months before the scheduled month of
delivery of each affected Aircraft, Boeing will increase or decrease the Advance
Payment Base Price of such Aircraft as required to reflect the effects of (i)
any adjustments in the Aircraft Basic Price pursuant to this Agreement and (ii)
the then-current forecasted escalation factors used by Boeing. Boeing will
provide the adjusted Advance Payment Base Prices for each affected Aircraft to
Buyer, and the advance payment schedule will be considered amended to substitute
such adjusted Advance Payment Base Prices.


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