The Comedy Central host told Letterman on CBS' "Late Show" on Tuesday he's going to do whatever Letterman has done. Letterman urges against it, saying, "You don't want to do that."
Letterman greeted Colbert warmly and offered an endorsement, saying CBS "could have just as easily hired another boob" like him.
Letterman is retiring next year. The "Late Show" released a 90-second clip of Colbert's appearance, taped for broadcast Tuesday night.