“It’s the biggest part of our cocktail business,” said Chance Robertson, operations director for Trudy’s, a local Mexican restaurant group. “It’s why people come here.” Mr. Robertson estimated that the three Trudy’s locations sell a total of 5,000 to 8,000 Mexican Martinis a week.

While the name gives it an air of mystique, originally the Mexican Martini was just a large margarita. But its presentation calls for the margarita to be served in a martini glass, with olives on a spear. Because it is about twice as large as a regular drink, customers are usually given the cocktail shaker and invited to pour the drink themselves.

A city with down-home Texas character, Austin also sports a veneer of cosmopolitan refinement that comes with being the seat of the state government and home to one of the country’s largest universities. In that light, the appeal of the Mexican Martini makes sense. While slurpy, frozen margaritas are a staple around the city, this one is dressed up in a suit and tie.

“It just looks cool,” said Jim LeMond, who worked at the Cedar Door for almost 20 years before opening the Barton Springs Saloon five years ago. “Yes, it’s just a margarita with olives, but you look real sophisticated when you’re pouring it yourself. There’s a ritual. On a table, it looks really classy.”

The story of its origin is a bit hazy, but Mr. LeMond said he thought that in the late ’70s or early ’80s, a Cedar Door bartender named Ellen was served a margarita in a martini glass while visiting Matamoros, Mexico, a border town. She brought the idea back to the bar, which at the time was a hangout for the city’s power brokers. The olives, he said, were an original Cedar Door touch.