SECURITIES AND EXCHANGE COMMISSION

                            Washington, D.C. 20549

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                                   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








      On or about March 18, 2004, the Board of Directors of the Company approved
an Amendment No. 2 (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 accelerate the Final Expiration Date (as defined in the
Rights Agreement). This Amendment No. 3 to Form 8-A is filed to reflect such
Amendment.

Item 2.  Exhibit.

1.    Amendment No. 2 to the Amended and Restated Rights Agreement dated as of
      March 29, 2004.


                                   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: March 31, 2004                     By:  /s/ Gary C. Kelly
                                              Gary C. Kelly
                                              Executive Vice President and
                                              Chief Financial Officer
                                              (Principal Financial and
                                              Accounting Officer)




























                                     EXHIBIT INDEX


EXHIBIT
NUMBER      DESCRIPTION


1.          Amendment No. 2 to the Amended and Restated Rights Agreement dated
            as of March 29, 2004.