The popular image of a cowboy would not be complete without the wide-brimmed “10-gallon hat,” yet even the most hardened cattlemen can’t agree on how the iconic headgear first got its name.

The conventional explanation is that “10-gallon” refers to how much liquid could be carried inside the hat. In fact, a famous ad for the Stetson company once even depicted a cowpoke giving his weary horse a drink from the crown of his hat.

While it’s certainly in keeping with the romantic conception of life in the Old West, this image is probably as much of a myth as gunfights at high noon. Not only is the name “10-gallon hat” an obvious exaggeration—even the most comically large cowboy hats could only hold a few quarts of water—carrying liquid in the crown of any hat would most likely damage it beyond repair.

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Most experts argue that the name “10-gallon hat” is actually an import from south of the border. Cattle drivers and ranchers in Texas and the Southwest often crossed paths with Mexican vaqueros who sported braided hatbands—called “galóns” in Spanish—on their sombreros. A “10 galón” sombrero was a hat with a large enough crown that it could hold 10 hatbands, but American cowboys may have anglicized the word to “gallon” and started referring to their own sombrero-inspired headgear as “10-gallon hats.”

Yet another linguistic theory argues that the name is a corruption of the Spanish phrase “tan galán” —roughly translated as “very gallant” or “really handsome”—which may have been used to describe the majestic image of a hat-wearing cowboy in the saddle.

Whatever its origin, the 10-gallon hat wasn’t even the preferred headgear for most people in the Wild West—top hats and bowlers were more common. The nickname didn’t enter the popular lexicon until the 1920s, when silent film stars like Tom Mix and Tim McCoy helped popularize the oversized hat in Hollywood Westerns. The 10-gallon hat went on to earn a place as a quintessential piece of the frontier wardrobe, and presidents like Harry Truman and Lyndon B. Johnson would later use them to cultivate a rustic image while serving as commander in chief.