Exhibit 99.1

January 31, 2011

Gary C. Kelly

2702 Love Field Dr.

Dallas, TX 75235-1611

Dear Gary:

The purpose of this letter is to confirm our agreement (the “ Agreement ”), effective as of February 1, 2011 (the “ Effective Date ”), concerning the continuation of certain provisions of the Employment Contract, effective as of July 15, 2007, and amended and restated as of November 20, 2008, by and between you and Southwest (the “ Employment Contract ”). Specifically, this Agreement provides for the continuation of the deferred compensation arrangement set forth in Paragraph IV-C of the Employment Contract (the “ Deferred Compensation Plan ”), effective as of the Effective Date. This Agreement will continue in existence until your Separation from Service (as defined below) with Southwest, unless earlier terminated at the direction of the Compensation Committee of the Board; provided that your right to receive payment pursuant to the Deferred Compensation Plan shall remain in effect until all payments due to you have been made. The period from the Effective Date to the date of your Separation from Service with Southwest is hereinafter referred to as the “ Term .” This Agreement may be amended in writing with the mutual consent of you and Southwest.

During the Term, Southwest will continue to set aside on its books, as currently provided in Paragraph IV-C of your Employment Contract (including your Employment Contract in the form effective as of July 15, 2004 (the “ Old Contract ”)), a special ledger Deferred Compensation Account (the “ Account ”) for you, and will credit thereto deferred compensation determined as hereinafter provided (“ Deferred Compensation ”). For each full or partial calendar year that you remain in the employment of Southwest during the Term, Deferred Compensation will accumulate in an amount equal to any contributions (including forfeitures but excluding any elective deferrals actually returned to you) which would otherwise have been made by Southwest on your behalf to the Southwest Airlines Co. Profitsharing Plan and Southwest Airlines Co. 401(k) Plan, but which exceed the amount permitted to be so contributed due to the limitations under Sections 415(c) (the “ 415(c) Excess Amount ”) and 401(a)(17) of the Internal Revenue Code (the “ Code ”). If your employment terminates prior to December 31 of any calendar year, Deferred Compensation will nonetheless accumulate for such year to the extent you are otherwise entitled to an allocation of the “Company Contribution” to the Southwest Airlines Co. ProfitSharing Plan for such year in accordance with the terms of the ProfitSharing Plan. In such case, Deferred Compensation will be calculated for such year as provided above. You hereby elect not to invest the 415(c) Excess Amount in Southwest’s 2005 Excess Benefit Plan (or any successor plan) for each calendar year during any part of which this Agreement is effect. The Deferred Compensation credited to the Account (including the Interest hereinafter provided) will be paid to you at the rate of $200,000 per calendar year (subject to

such payroll and withholding deductions as may be required by law), commencing with the calendar year following the year in which (i) you become sixty-five (65) or (ii) you incur a “separation from service,” within the meaning of Treasury Regulation §1.409A-1(h), with Southwest (a “ Separation from Service ”), whichever occurs later, and continuing until the entire amount of Deferred Compensation and Interest credited to the Account has been paid. Although the total amount of Deferred Compensation ultimately payable to you hereunder will be computed in accordance with the provisions set forth above, there will be accrued and credited to the Account, beginning on January 1, 2007 (if not so accrued and credited pursuant to the Old Contract, and if so accrued and credited, then beginning on January 1, 2008) and continuing annually thereafter until the entire balance of the account has been distributed (whether such distribution takes place during the Term or thereafter), amounts equal to simple interest at the rate of ten percent (10%) per annum, compounded annually (“ Interest ”), on the accrued and unpaid balance of the Deferred Compensation credited to the Account as of the preceding December 31. The Deferred Compensation and Interest to be paid in any one calendar year will be paid on the first business day of such calendar year; provided, however, that if the event triggering commencement of payment of Deferred Compensation and Interest is your Separation from Service, payment of the first of such annual Deferred Compensation and Interest payments will be deferred to the extent necessary to cause such payment to comply with the six month deferral rule described in Section 409A(a)(2)(B) of the Code if you are a “specified employee” within the meaning of such section at the time of your Separation from Service. Notwithstanding the foregoing, in the event of your death, then the unpaid balance of the Deferred Compensation (together with any accrued Interest thereon) will be paid to the executors or administrators of your estate in cash in one lump sum on the first business day of the calendar year next following the calendar year in which your death occurred. Southwest at its election may fund the payment of Deferred Compensation by setting aside and investing such funds as Southwest may from time to time determine. Neither the establishment of the Account, the crediting of Deferred Compensation thereto, nor the setting aside of any funds will be deemed to create a trust. Legal and equitable title to any funds set aside will remain in Southwest, and you will have no security or other interest in such funds. Any funds so set aside or invested will remain subject to the claims of the creditors of Southwest, present and future. No right, title, interest or benefit under this paragraph will ever be liable for or charged with any of the torts or obligations of you or any person claiming under you, or be subject to seizure by any creditor of you or any person claiming under you. Neither you nor any person claiming under you will have the power to anticipate or dispose of any right, title, interest or benefit under this paragraph in any manner until the same is actually distributed by Southwest.

Payments made pursuant to this Agreement will be subject to applicable tax withholding. Effective as of the Effective Date hereof you agree that your Employment Contract is terminated and will be of no force and effect and that the benefits previously payable under your Employment Contract and set forth in this Agreement will be, as of the Effective Date, provided pursuant to the terms of this Agreement. Notwithstanding the foregoing, nothing in this Agreement is intended to result in the termination of the Deferred Compensation Plan for purposes of Section 409A of the Code and nothing in this Agreement is intended to change the time or form of benefit available under the Deferred Compensation Plan. This Agreement will be subject to and governed by the laws of the State of Texas, without giving effect to any conflict of law provisions thereof, except to the extent Texas law is preempted by federal law.

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By signing below, you agree that this letter agreement accurately reflects our mutual agreements with respect to the Deferred Compensation Plan. This Agreement may be signed in multiple counterparts, each of which will be deemed an original but all of which taken together will constitute a single instrument.

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