FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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(Print or Type Responses)

1. Name and Address of Reporting Person * BARRETT COLLEEN C   2. Issuer Name and Ticker or Trading Symbol SOUTHWEST AIRLINES CO [LUV] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) President (Last) (First) (Middle) C/O SOUTHWEST AIRLINES CO, P O BOX 36611 3. Date of Earliest Transaction (Month/Day/Year) 10/14/2004 (Street) DALLAS, TX 75235 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock 10/14/2004   M   25,786 A $ 3.72 120,530 D   Common Stock 10/14/2004   M   4,214 A $ 4.98 124,744 D   Common Stock 10/14/2004   F   5,728 D $ 14.02 119,016 D   Common Stock 10/14/2004   F   8,337 D $ 14.02 110,679 D   Common Stock               1,492 I Profit Sharing (2)

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Option (Right to Buy)

$ 14.95

10/14/2004

A

50,000

07/15/2004

07/15/2014

Common Stock

50,000

$ 14.95

50,000 (1)

D

Option (Right to Buy)

$ 14.95

10/14/2004

A

50,000

07/15/2005

07/15/2014

Common Stock

50,000

$ 14.95

100,000 (1)

D

Option (Right to Buy)

$ 14.95

10/14/2004

A

50,000

07/15/2006

07/15/2014

Common Stock

50,000

$ 14.95

150,000 (1)

D

Option (Right to Buy)

$ 3.72

10/14/2004

M

25,786 (3)

01/26/1996

01/26/2005

Common Stock

25,786

$ 3.72

0

D

Option (Right to Buy)

$ 4.98

10/14/2004

M

4,214 (4)

01/26/1998

01/26/2006

Common Stock

4,214

$ 4.98

33,087

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
BARRETT COLLEEN C C/O SOUTHWEST AIRLINES CO P O BOX 36611 DALLAS, TX 75235			President

Signatures

On behalf of and attorney-in-fact for Colleen C. Barrett /s/ Deborah Ackerman		10/15/2004
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	Options granted from the 1996 ISO Plan.
(2)	The information reported herein is based on a plan statement dated as of December 31, 2003.
(3)	Options granted from the 1995 NQ Plan.
(4)	Options granted from the 1996 NQ Plan.

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