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                       SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549

                                   ----------

                                    FORM 8-A
                                 AMENDMENT NO. 3
                                (File No. 1-7259)


                FOR REGISTRATION OF CERTAIN CLASSES OF SECURITIES
                     PURSUANT TO SECTION 12(b) OR (g) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

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                             SOUTHWEST AIRLINES CO.
             (Exact name of registrant as specified in its charter)


                TEXAS                                           74-1563240
(State of Incorporation or organization)                      (I.R.S. Employer
                                                          Identification Number)


            P.O. BOX 36611
             DALLAS, TEXAS                                      75235-1611
    (Address of principal executive offices)                    (Zip code)


Securities to be registered pursuant to Section 12(b) of the Act:

    Title of each class                        Name of each exchange on which
    to be so registered                        each class is to be registered
    -------------------                        ------------------------------

    COMMON SHARE RIGHTS                           NEW YORK STOCK EXCHANGE


If this Form relates to the registration of a class of securities
pursuant to Section 12(b) of the Exchange Act and is effective
pursuant to General Instruction A.(c),check the following box. [X]

If this Form relates to the registration of a class of securities pursuant to
Section 12(g) of the Exchange Act and is effective pursuant to General
Instruction A.(d), check the following box.[ ]


Securities to be registered pursuant to Section 12(g) of the Act:  NONE


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         On or about March 15, 2001, the Board of Directors of the Company
approved an Amendment No. 1 (the "Amendment") to its Amended and Restated Rights
Agreement dated as of July 18, 1996 (the "Rights Agreement"). The Board amended
the Rights Agreement to (a) accelerate the Final Expiration Date (as defined in
the Rights Agreement) and (b) to make the provisions of such agreement
inapplicable to certain fully-financed cash tender offers (as more fully
described in the Amendment) for the common stock of the Company. This Amendment
No. 3 to Form 8-A is filed to reflect such Amendment.


Item 2.  Exhibit.

1.       Amendment No. 1 to the Amended and Restated Rights Agreement
         dated as of March 15, 2001.







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                                    SIGNATURE

         Pursuant to the requirements of Section 12 of the Securities Exchange
Act of 1934, the registrant has duly caused this report to be signed on its
behalf by the undersigned hereunto duly authorized.


                                           SOUTHWEST AIRLINES CO.



Date: April 25, 2001                       By:  /s/ Gary C. Kelly
                                              ----------------------------------
                                              Gary C. Kelly
                                              Vice President - Finance and
                                              Chief Financial Officer
                                              (Principal Financial and
                                              Accounting Officer)




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                                  EXHIBIT INDEX




EXHIBIT
NUMBER       DESCRIPTION
------       -----------
      
1.       Amendment No. 1 to the Amended and Restated Rights Agreement dated as
         of March 15, 2001.




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