But Ms. Barrett, who steps down from her president's job at midnight today, knows what the label means.
"I'm OK with Mom," Ms. Barrett said last week. "I'm OK with Grandma. That's what I said at the shareholders' meeting [May 21]. It's time for me to take the next step with grandmotherhood."
Like her longtime boss, Herb Kelleher, who gave up his chairman's job in May, Ms. Barrett is leaving her executive's job but staying with the airline for at least five years, with duties to be defined by chief executive Gary Kelly.
Ms. Barrett has been a primary architect of Southwest's people-friendly culture since she began working full time for the airline in 1981.
She'd like to keep a focus on that in her new life as just another employee - as long as Mr. Kelly agrees.
"I want to be part of it," she said. "But it's only fair to Gary - I really feel strong about this - that it's time for me to follow."
Ms. Barrett's long path to the president's office began 41 years ago when she was a 23-year-old legal secretary looking for a job in San Antonio.
The Vermont native joined an established law firm that included another East Coast transplant, Herb Kelleher, and his disorganized office.
"Actually, I discovered Herb," she said. "Really and truly. I laugh about it. I found this man. He needed help. It was clear. I was going to be his savior."
From the time she began helping Mr. Kelleher in 1967, Ms. Barrett found herself doing legal work for this little airline being started by one of his clients, San Antonio businessman Rollin King.
After a bruising, vicious legal battle, Southwest finally started flying passengers on June 18, 1971. Then, in 1978, the first chief executive, Lamar Muse, resigned in a boardroom battle, pushing Mr. Kelleher - and right-hand person Colleen Barrett - into a much more active role.
Mr. Kelleher became chairman, even as he kept up as much of his San Antonio law practice as possible. And for the eight months it took to get a new CEO in place, he and Ms. Barrett would work all week in Dallas, then fly home to San Antonio on the weekend.
Then, in 1981, Mr. Muse's replacement as president and CEO, Howard Putnam, quit to join Braniff International Airways. Mr. Kelleher took the chief executive's and president's job as well, and Ms. Barrett moved to Dallas.
From there, the legend of the Herb-and-Colleen show grew. Herb was this brilliant, flamboyant executive; Colleen was the assistant who kept him organized, on focus, on time.
But as she was helping Mr. Kelleher, she was putting her own stamp on the airline, making sure that the carrier did the right thing for its employees.
The underlying principle was that if the airline took care of its employees, the employees would take care of the customers, and the shareholders would win, too.
In 1986, she was named vice president of administration; then, in 1990, executive vice president of customers.
In 2001, as Mr. Kelleher prepared to step back from some of his responsibilities, the board of directors named general counsel Jim Parker chief executive and Ms. Barrett president and chief operating officer.
The new titles helped the world understand that Ms. Barrett had played a key part in making Southwest what it has become.
For the formal legal secretary, the realization of what she has become conflicts with her modest opinion of herself.
On one hand, she has had to fight for years to make people inside Southwest and out understand that she had her own opinions and expertise, and that she isn't just a conduit for what Mr. Kelleher thinks.
For many, she said, "once Herb's secretary, I was always Herb's secretary."
Former American Airlines Inc. chief Bob Crandall introduced her as "Herb's secretary" maybe six years ago, she said, long after she had become a top executive at Southwest.
"I never corrected people on that. It wasn't particularly offensive to me. But I remember thinking, why do people think that anything that I say is just a parrot of what Herb thinks?"
On June 18, Ms. Barrett found herself at a Wharton School of Business leadership conference.
"Everyone was a chief executive officer except for me, first of all," Ms. Barrett said. "Secondly, they were famous, well-known names. I was like, 'Holy moley.' And I was the only woman."
As she relinquishes her job as president, Ms. Barrett expects to be able to accept more such invitations. She has agreed to co-chair capital fundraising for Becker College, the Worcester, Mass., school where she received her associate's degree.
She's also joined the advisory board of the Ken Blanchard College of Business at Grand Canyon University in Phoenix.
She intends to take time for her friends, take real vacations, actually take Saturdays and Sundays off.
And at Southwest, she wants to simply contribute to the company that has been a part of almost all her adult life.
"I want for people to think of me really as an employee," Ms. Barrett said. "I'm no different today than I was in 1967. I still want to be part of the team."
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