AMENDMENT NO. 1 TO SOUTHWEST AIRLINES CO. EXCESS BENEFIT PLAN

Exhibit 10.33

AMENDMENT NO. 1

TO

SOUTHWEST AIRLINES CO. EXCESS BENEFIT PLAN

Pursuant to the authority of the Board of Directors of Southwest Airlines Co., and the provisions of Article X thereof, the Southwest Airlines Co. Excess Benefit Plan is hereby amended, effective as of December 31, 2004, in the following respects only:

Article XII is hereby amended to add Section 12.6 to read as follows:

“12.6 Suspension of Certain Credits. Notwithstanding any provision of this Plan to the contrary, the Plan shall be frozen and all amounts which, on or after January 1, 2005, would otherwise be credited pursuant to Section 3.1 hereof shall be suspended to the extent crediting any such amount would result in a deferral of compensation to which Section 409A of the Code applies.”

IN WITNESS WHEREOF, and as conclusive evidence of the adoption of the foregoing instrument comprising Amendment No. 1 to Southwest Airlines Co. Excess Benefit Plan, the Company has caused these presents to be duly executed in its name and behalf by its proper officers thereunto duly authorized effective as of the 31^st day of December 2004.

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BEFORE ME, the undersigned, a Notary Public in and for said County and State, on this 15^th day of December, 2005, personally appeared GARY C. KELLY, to me known to be the identical person who subscribed the name of SOUTHWEST AIRLINES CO., as its CHIEF EXECUTIVE OFFICER to the foregoing instrument and acknowledged to me that he executed the same as his free and voluntary act and deed and as the free and voluntary act and deed of such organization for the uses and purposes therein set forth.

GIVEN UNDER MY HAND AND SEAL OF OFFICE, the day and year last above written.

My Commission Expires: June 4, 2006

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