ADVISORY AND NON-COMPETE/NON-SOLICITATION AGREEMENT

Exhibit 10.29

ADVISORY AND NON-COMPETE/NON-SOLICITATION AGREEMENT

This Advisory and Non-Compete/Non-Solicitation Agreement (“Agreement”) is made and entered into by and between Southwest Airlines Co. (“Company”), and Laura Wright (“Advisor”) effective as January 31, 2013.

1. Termination of Employment and Advisory Period.

(a) Advisor voluntarily terminated her employment with the Company effective as of January 31, 2013 (the “Separation Date”).

(b) From the Separation Date and for a period of six months following such date (“Consulting Period”), Advisor shall provide consulting services necessary for the transition of Advisor’s duties while she was an employee of the Company and on special projects, as requested by the Chief Executive Officer of the Company. The level of services to be performed by Advisor during the Consulting Period will not exceed a level equal to 20% of the average level of services performed by Advisor during the 36-month period immediately preceding the Separation Date.

(c) Advisor shall be an independent contractor and not an agent or employee of the Company. Neither the relationship of the Company and Advisor nor any provision of this Agreement shall be construed to authorize Advisor to take any action, make or fail to make any decision, representation or commitment, binding upon the Company or any of its affiliated companies in the absence of written specific authorization executed by an executive officer of the Company. The Company shall at all times be free to employ other consultants to perform services in addition to or in lieu of the services to be provided by Advisor. Subject to the provisions of this Agreement, Advisor shall be free to devote such time, energy and skill during regular business hours as she is not obligated to devote hereunder to the Company in such manner as she deems fit and to such persons, firms or corporations as she chooses.

2. Confidentiality, Non-Compete and Non-Solicitation Obligations.

(a) The Advisor acknowledges that the Company has trade, business and financial secrets and other confidential and proprietary information (collectively, the “Confidential Information”). Confidential information includes, but is not limited to, sales materials, technical information, strategic information, business plans, processes and compilations of information, records, specifications and information concerning customers or venders, customer lists, and information regarding methods of doing business. As defined herein, Confidential Information shall not include information that is generally known to other persons or entities who can obtain economic value from its disclosure or use.

(b) The Advisor is aware of those policies implemented by the Company to keep its Confidential Information secret, including those policies limiting the disclosure of information on a need-to-know basis, requiring the labeling of documents as “confidential,” and requiring the keeping of information in secure areas. The Advisor acknowledges that the Confidential Information has been developed or acquired by the Company through the expenditure of substantial time, effort and money and provides the Company with an advantage over competitors who do not know or use such Confidential Information.

(c) During and following the Consulting Period, the Advisor shall hold in confidence and not directly or indirectly disclose or use or copy or make lists of any Confidential Information except to the extent authorized in writing by the Chief Executive Officer or compelled by legal process, other than to an employee of the Company or a person to whom disclosure is reasonably necessary or appropriate in connection with the performance by the Advisor of her duties pursuant to this Agreement. The Advisor agrees to use reasonable efforts to give the Company notice of any and all attempts to compel disclosure of any Confidential Information, in such a manner so as to provide the Company with written notice at least five days before disclosure or within one business day after the Advisor is informed that such disclosure is being or will be compelled, whichever is earlier. Such written notice shall include a description of the information to be disclosed, the court, government agency, or other forum through which the disclosure is sought, and the date by which the information is to be disclosed, and shall contain a copy of the subpoena, order or other process used to compel disclosure.

(d) The Advisor further agrees not to use any Confidential Information for the benefit of any person or entity other than the Company.

(e) All records, files, documents and materials, or copies thereof, relating to the Company’s and its affiliates’ business which the Advisor shall prepare, or use, or be provided with as a result of the Agreement or which the Advisor has prepared, or used, or been provided with as a result of her employment with the Company, shall be and remain the sole property of the Company or its affiliates, as the case may be, and shall be returned promptly by the Advisor to the owner upon termination of the Consulting Period.

(f) The Advisor acknowledges and agrees that the nature of the Confidential Information which the Company provided to her by the Company during the term of her employment, and commits to provide to her during the Consulting Period, would make it difficult, if not impossible, for her to perform in a similar capacity for a Competing Business (as defined below) without disclosing or utilizing the Confidential Information. The Advisor further acknowledges and agrees that the Company’s business is conducted throughout the country in a highly competitive market. Accordingly, the Advisor agrees that she will not (other than for the benefit of the Company pursuant to this Agreement) directly or indirectly, individually or as an officer, director, employee, shareholder, consultant, contractor, partner, joint venturer, agent, equity owner or in any capacity whatsoever (1) during the term of Non-Competition, engage in the airline business or in any other business activity that the Company is conducting, or is intending to conduct, on the Separation Date in any geographical area in which the Company conducts business (a “Competing Business”), or (2) during the Term of Non-Solicitation, (i) hire, attempt to hire, or contact or solicit with respect to hiring any employee of the Company, or (ii) solicit, divert or take away any customers or customer leads (as of the end of the Consulting Period) of the Company. The “Term of Non-Competition” and the “Term of Non-Solicitation” shall each be defined as that term beginning on the Separation Date and continuing until the three-year anniversary of the Separation Date.

(g) During the Consulting Period the Company shall provide the Advisor with Confidential Information of the Company as described in Section 2(a). Accordingly, in consideration for the Company’s commitment to provide Confidential Information to the Advisor and the Consideration and in order to protect the value of the Confidential Information

to the Company, the Advisor agrees that during the Term of Non-Competition or the Term of Non-Solicitation, she will not directly or indirectly disclose or use or disclose for any reason whatsoever any Confidential Information obtained by reason of her employment or consulting relationship with the Company or any predecessor, except as required to conduct the business of the Company. The obligations of the Advisor set forth in the preceding sentence are in addition to, and not in lieu of, the obligations of the Advisor set forth in Section 2(c) of this Agreement.

(h) During the Term of Non-Competition, the Advisor will not use the Advisor’s access to, knowledge of, or application of Confidential Information to perform any duty for any Competing Business; it being understood and agreed to that this Section 2(h) shall be in addition to and not be construed as a limitation upon the covenants in Section 2(f) hereof.

(i) The Advisor acknowledges that the geographic boundaries, scope of prohibited activities, and time duration of the preceding paragraphs are reasonable in nature and are no broader than are necessary to maintain the confidentiality and the goodwill of the Company and the confidentiality of its Confidential Information and to protect the other legitimate business interests of the Company.

(j) If any court determines that any portion of this Section 2 is invalid or unenforceable, the remainder of this Section 2 shall not thereby be affected and shall be given full effect without regard to the invalid provisions. If any court construes any of the provisions of this Section 2, or any part thereof, to be unreasonable because of the duration or scope of such provision, such court shall have the power to reduce the duration or scope of such provision and to enforce such provision as so reduced.

(k) The Advisor’s covenants under this Section 2 of the Agreement shall be construed as an agreement independent of any other provision of this Agreement; and the existence of any claim or cause of action of Advisor against the Company, whether predicated on this Agreement or otherwise, shall not constitute a defense to the enforcement by the Company of this covenant.

(l) The parties shall execute such documents and take such other action as is necessary or appropriate to effectuate the provisions of this Agreement.

(m) As used in this Section 2 and in Section 4, “Company” shall include Southwest Airlines Co. and any of its affiliates.

3. Consideration.

(a) In consideration for Advisor’s promises herein and provided that the Advisor continues to comply with the restrictive covenants set forth in Section 2, the Company shall:

(i) Pay Advisor $40,000 for each month of the six month Consulting Period (the “Advisory Fee”), on the last regular pay date of each calendar month beginning in February 2013 and ending in July 2013. The Company will not withhold from the Advisory Fee any sums for income tax, unemployment insurance, social security, or any other withholding pursuant to any law, nor will the Company make available to Advisor any of the benefits

afforded to employees of the Company other than retirement benefits available to her due to her age and service and group health plan continuation coverage, to the extent Advisor timely elects pursuant to the Consolidated Omnibus Budget Reconciliation Act of 1985, as amended. Advisor expressly acknowledges and agrees that Advisor is solely responsible for the payment of all income and other taxes associated with the Advisory Fee.

(ii) Upon the execution and delivery of release (in the form attached Exhibit A) on or prior to July 31, 2013 (and not subsequently revoked), in consideration for the Advisor’s covenants set forth in Section 2, pay Advisor an amount equal to $1,821,600 on the first regular pay date in August 2013. The Company will withhold from the amounts payable pursuant to this Section 3(a)(ii) all federal, state, city, or other income or employment taxes as may be required pursuant to any law or governmental regulation or ruling.

(iii) In accordance with the terms of the Company’s Amended and Restated 2007 Equity Incentive Plan and the related terms and conditions applicable to Advisor’s restricted stock unit grants, provide for the continued vesting of restricted stock units held by the Advisor during the Consulting Period. The Company will withhold with respect to such restricted stock units all federal, state, city, or other income or employment taxes as may be required pursuant to any law or governmental regulation or ruling.

(iv) Provide (A) Advisor and her spouse with lifetime unlimited NRMR and NRSA travel and (B) any “qualifying child” (as defined in section 152(c) of the Internal Revenue Code of 1986, as amended, (the “Code”)) of Advisor with NRSA travel, in each case, on Southwest Airlines and AirTran in accordance with the Company policy in effect from time to time regarding retiree travel for former officers of the Company, such benefit (in the case of NRMR travel) commencing on the date that is six months following the Separation Date. Also on such date, Advisor shall be reimbursed for her cost in purchasing positive space airfare during the six-month period for herself and her spouse. Advisor agrees to provide timely notice to the Company of any such expenses (and any other documentation that the Company may reasonably require to substantiate such expenses) in order to facilitate the Company’s timely reimbursement of the same. The reimbursement pursuant to this Section 3(c)(iv) is not subject to liquidation or exchange for another benefit and the amount of such reimbursement is payable only in 2013 and is not payable in, and will not affect the amount of any reimbursements that Advisor may receive in, any other taxable year.

(b) The consideration set forth in this Section 3 is referred to as the “Consideration.”

4. Cooperation Post-Employment. During and following the Consulting Period, Advisor will cooperate with and assist the Company in defense of any claim, litigation or administrative proceeding brought against the Company, as reasonably requested by the Company. Such cooperation and assistance shall include, but not be limited to, (i) interviews of Advisor by legal counsel for the Company as reasonably requested by such counsel, (ii) Advisor providing documents (or copies thereof) and executing affidavits as reasonably requested by such counsel, (iii) Advisor appearing for depositions, trials, and other proceedings as reasonably requested by such counsel, and (iv) Advisor communicating with any party adverse to the Company, or with a representative, agent or legal counsel for any such party, concerning any

pending or future claims or litigation or administrative proceeding solely through legal counsel for the Company. The Company will pay all reasonable out-of-pocket expenses incurred by Advisor in providing such cooperation and assistance, provided such expenses have been pre-approved by the Company. Nothing in this paragraph 4 is intended to cause Advisor to testify other than truthfully in any proceeding or affidavit.

5. Warranties and Other Obligations of Advisor. Advisor agrees, represents and warrants that:

(a) The Consideration is not something to which Advisor is otherwise indisputably entitled, is good and sufficient consideration for Advisors execution and non-revocation of this Agreement.

(b) Advisor is legally and mentally competent to sign this Agreement.

(c) Advisor presently possesses the exclusive right to receive all of the Consideration paid in exchange for this Agreement.

6. Choice of Law. This Agreement shall be interpreted and construed in accordance with and shall be governed by the laws of the State of Texas (without regard to any conflicts of law principle which would require the application of some other state law) and, when applicable, the laws of the United States.

7. Entire Agreement. This Agreement constitutes the entire agreement of the parties relating to the subject matter hereof. Any previous agreements with respect to this subject matter are superseded by this Agreement and are of no further force or effect, provided that Advisors continuing obligations under the Employment Agreement shall remain in full force and effect according to its terms. No term, provision or condition of this Agreement may be modified in any respect except by a writing executed by both Advisor and the Company. No person has any authority to make any representation or promise on behalf of any of the parties not set forth in this Agreement. This Agreement has not been executed in reliance upon any representation or promise except those contained herein.

8. Acknowledgment of Terms. Advisor acknowledges that Advisor has carefully read this Agreement; that Advisor has had the opportunity for review of it by Advisor’s attorney; and that Advisor is signing this Agreement voluntarily.

9. Waiver. The failure of either party to enforce or to require timely compliance with any term or provision of this Agreement shall not be deemed to be a waiver or relinquishment of rights or obligations arising hereunder, nor shall this failure preclude the enforcement of any term or provision or avoid the liability for any breach of this Agreement.

10. Severability. Each part, term or provision of this Agreement is severable from the others. Notwithstanding any possible future finding by a duly constituted authority that a particular part, term or provision is invalid, void or unenforceable, this Agreement has been made with the clear intention that the validity and enforceability of the remaining parts, terms and provisions shall not be affected thereby.

11. Construction. This Agreement shall be deemed drafted equally by all the parties. Its language shall be construed as a whole and according to its fair meaning. Any presumption or principle that the language is to be construed against any party shall not apply. The headings in this Agreement are only for convenience and are not intended to affect construction or interpretation. The plural includes the singular and the singular includes the plural; “and” and “or” are each used both conjunctively and disjunctively; “any,” “all,” “each,” or “every” means “any and all, and each and every;” “including” and “includes” are each “without limitation;” and “herein,” “hereof,” “hereunder” and other similar compounds of the word “here” refer to the entire Agreement and not to any particular paragraph, subparagraph, section or subsection.

12. Timing. Advisor acknowledges and agrees Advisor has had a reasonable time to consider this Agreement before executing it.

13. Advice to Consult Counsel. The Company hereby advises Advisor to consult with an attorney prior to executing this Agreement.

14. Survival. The respective rights and obligations of the parties hereunder shall survive any termination of this Agreement to the extent necessary to the intended preservation of such rights and obligations. The provisions of this Section are in addition to the survivorship provisions of any other section of this Agreement.

15. Counterparts. This Agreement may be executed in several counterparts, each of which shall be deemed to be an original, but all of which together will constitute one and the same Agreement. Signatures delivered by facsimile shall be deemed effective for all purposes.

16. Section 409A. This Agreement is intended to be exempt from or compliant with Section 409A of the Code and the provisions of this Release shall be construed accordingly. Advisor’s “separation from service” within the meaning of Treasury Regulation § 1.409A-1(h) was January 31, 2013.

17. Notices. All notices and other communications hereunder shall be in writing and shall be given by hand delivery to the other party or by registered or certified mail, return receipt requested, postage prepaid, or by facsimile, as follows:

If to Advisor:           Laura Wright

                                 [HOME ADDRESS]

If to the Company:   Southwest Airlines Co.

   2702 Love Field Drive, HDQ-4GC

   Dallas, Texas 75235

   Attn: Vice President, General Counsel

or to such other address as either party shall have furnished to the other in writing in accordance herewith. Notice and communications shall be effective when actually received by the addressee.

REMAINDER OF PAGE INTENTIONALLY LEFT BLANK

EXHIBIT A

GENERAL RELEASE OF CLAIMS

This General Release of Claims (the “Release”) is entered into between Laura Wright (“Advisor”) and Southwest Airlines Co. (the “Company”). For and in consideration of the mutual covenants and promises set out in this Release, and for other good and valuable consideration, the receipt and sufficiency of which are acknowledged, Advisor and the Company agree:

Section 1. Date of Termination. Advisor’s employment with the Company terminated on January 31, 2013 and Advisor’s service relationship as an independent contractor terminated as of July 31, 2013 (the “Termination Date”).

Section 2. Non-Compete/Non-Solicitation Payment. Provided Advisor executes and delivers to the Company this Release no later than July 31, 2013 (the “Release Return Date”) and does not revoke it within seven days of execution, the Company agrees to pay to Advisor the amount set forth in Section 2(a)(ii) of the Advisory and Non-Compete/Non-Solicitation Agreement effective as of February 1, 2013, less appropriate, legally-required deductions, on the first regular pay date of the Company in August 2013.

Section 3. Company Property and Expenses. Advisor must return any materials or property (other than personal effects) that Advisor has acquired or prepared while employed by the Company and in connection with such employment including, without limitation, all computer hardware, software, documents (whether or not electronic), files, records, keys and any other Company equipment, materials, documents or other property on or before the Termination Date.

Section 4. Release.

A. Advisor agrees to, and hereby does, release and discharge the Company and any parent, subsidiary, predecessor, successor, assign or affiliated entity, along with their respective owners, partners, officers, members, directors, employees, agents, attorneys, successors, administrators and insurers (collectively the “Company Parties”), from any and all claims, demands, liabilities and causes of action, whether statutory or common law, including, but not limited to, any claim for salary, bonus, benefits, payments, expenses, costs, damages, penalties, compensation, remuneration, wages, contractual entitlements or pursuant to any employment agreement or similar agreement between Advisor and the Company, and all claims or causes of action relating to any matter occurring on or prior to the date that Advisor executed this Release, including without limitation any alleged violation of: (i) the Age Discrimination in Employment Act of 1967 and Older Worker’s Benefit Protection Act of 1990, as amended; (ii) Title VII of the Civil Rights Act of 1964, as amended; (iii) the Civil Rights Act of 1991; (iv) Sections 1981 through 1988 of Title 42 of the United States Code, as amended; (v) the Employee Retirement Income Security Act of 1974, as amended; (vi) the Immigration Reform Control Act, as amended; (vii) the Americans with Disabilities Act of 1990, as amended; (viii) the National Labor Relations Act, as amended; (ix) the Occupational Safety and Health Act, as amended; (x) the Family and Medical Leave Act of 1993, as amended; (xi) the Worker Adjustment and Retraining Notification Act; (xii) any state or federal anti-discrimination law; (xiii) any state or

federal wage and hour law; (xiv) any other local, state or federal law, regulation or ordinance; (xv) any public policy, contract, tort, or common law claim; (xvi) any allegation for costs, fees, or other expenses including attorneys’ fees incurred in the matters referenced herein; and (xvii) any and all claims Advisor may have arising as the result of any alleged breach of any contract, incentive compensation plan or agreement or stock option plan or agreement with any Company Party (collectively, the “Released Claims”). This Release extinguishes all rights, if any, which Advisor may have, contractual or otherwise, relating to or arising out of Advisor’s employment with the Company and the termination of Advisor’s employment. Advisor acknowledges that Advisor has received all leaves (paid and unpaid) to which Advisor was entitled during Advisor’s employment and, as of the date that Advisor executes this Release, Advisor has received all wages and been paid all sums (including bonuses) that Advisor is owed by the Company. This Release is not intended to indicate that any such claims exist or that, if they do exist, they are meritorious. Rather, Advisor is simply agreeing that, in exchange for the consideration described in Section 2 of this Release, any and all potential claims of this nature that Advisor may have against the Company Parties, regardless of whether they exist, are settled, compromised and waived.

B. Notwithstanding this release of liability, nothing in this Release prevents Advisor from filing any non-legally waivable claim, including a challenge to the validity of this Release with the Equal Employment Opportunity Commission (“EEOC”) or comparable state or local agency, or participating in any investigation or proceeding conducted by the EEOC or comparable state or local agency; however, Advisor understands and agrees that Advisor is waiving any and all rights to recover any monetary or personal relief or recovery as a result of such EEOC or comparable state or local agency proceeding or subsequent legal actions. Further, in no event shall the Released Claims include: (i) any claim which arises after the date this Release is executed by Advisor, including any claim to enforce Advisor’s rights under this Release; (ii) any claim to any vested benefits under an employee benefit plan; or (iii) any claim to enforce indemnification or expense advancement rights, if any, under any agreement or the Company’s charter or bylaws.

Section 5. Advisor’s Representation. Advisor has not brought or joined any claims, appeals, complaints, charges or lawsuits against any Company Party and has made no assignment, sale, delivery, transfer or conveyance of any rights Advisor has asserted or may have against any of the Company Parties with respect to any Released Claim.

Section 6. ADEA Rights. Advisor further acknowledges that:

A. Advisor has been advised that Advisor has the right to seek legal counsel before signing this Release and has had adequate opportunity to do so. Advisor warrants that Advisor executes this Release voluntarily and of Advisor’s own free will, after having a reasonable period of time to review and deliberate regarding its meaning and effect.

B. Advisor has been given at least 21 days to review this Release and understands that if Advisor does not accept this Release by returning an executed copy to the Company by the 22^nd day after this Release is provided to Advisor, this offer will expire.

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C. Advisor has seven days after signing this Release to revoke it. This Release will not become effective or enforceable until the revocation period has expired. Any notice of revocation of the Release is effective only if received by the Vice President, General Counsel, in care of the Company at 2702 Love Field Drive, HDQ-4GC, Dallas, Texas 75235, in writing by the close of business at 5:00 p.m. Central Standard Time on the seventh day after Advisor’s signing of this Release. If Advisor revokes Advisor’s acceptance of this Release pursuant to this Section 6C, the Company will not provide Advisor with any non-compete/non-solicitation payment described in Section 2 above and all other terms of this Release will become null and void.

D. Advisor acknowledges that Advisor is receiving, pursuant to this Release, consideration in addition to anything of value to which Advisor is already entitled.

Section 7. Section 409A. This Release is intended to be exempt from or compliant with Section 409A of the Internal Revenue Code of 1986, as amended, and the provisions of this Release shall be construed accordingly. Advisor’s “separation from service” within the meaning of Treasury Regulation § 1.409A-1(h) was January 31, 2013.

Section 8. Choice of Law, Modification and Execution. This Release will be construed in accordance with and governed by the laws of Texas. The parties agree that this Release cannot be modified or amended except by a written instrument signed by Advisor and a duly authorized representative of the Company. This Release may be executed in multiple parts.

Section 9. Entire Agreement. This Release sets forth the entire agreement between Advisor and the Company relating to the subject matter herein and supersedes any and all prior oral or written agreements or understandings between Advisor and the Company concerning the subject matter of this Release. Neither of the parties has made any settlement, representations or warranty in connection herewith (except those expressly set forth in this Release) that have been relied upon by the other party, or that acted as an inducement for the other party to enter into this Release

[Signature page follows]

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I ACKNOWLEDGE THAT I HAVE CAREFULLY READ THE FOREGOING AGREEMENT, UNDERSTAND ALL OF ITS TERMS, UNDERSTAND THAT IT CONTAINS A COMPLETE RELEASE OF ALL KNOWN AND UNKNOWN CLAIMS, AND AM ENTERING INTO IT VOLUNTARILY.

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