Agassi, who now shaves his head bald, recently revealed in his autobiography "Open" that he wore a hairpiece during his tennis-playing career.
"The night before the French Open final, I used the wrong conditioner and it started to come off," the athlete told Letterman.
"So now, you've got to play on clay -- the French Open is clay -- and you're worried you can lose your hair," Letterman remarked.
"Big time," Agassi said. "I've never prayed for results in my life, but I prayed that day for that wig to stay on. I mean, I had about 50 bobby pins holding it down, and I said to my brother: 'Is this going to stay? You know, I mean, it's my first Grand Slam finals.' And he says: 'I think it will. Just don't move around so much.'"
"That's right, it's tennis. Try not to move around," Letterman joked. "See if they'll just hit it right to you."
Referring to Agassi's mullet-style weave, Letterman asked, "But why that number there?"
"Well, you know, it's a good question," Agassi replied. "I was at a time in my life, too, where I was kind of, in a bit, hiding myself. You know, I think any form of rebellion is really somebody trying to, you know, hide who they really are, their inner self, and I think what better way to hide yourself than to wear a mullet."
CBS said Letterman had the hairpiece lowered on stage from the rafters of the Ed Sullivan Theater where the "Late Show" is taped. Agassi held it one final time, then presented it to a woman in the audience who was celebrating her birthday.