Credit: Jeffrey R. Staab/AP Photo.

On Thursday's "Late Show with David Letterman," Conan O'Brien made his first appearance on the show in 13 years. Conan's short-lived stint as host of NBC's "The Tonight Show," from which he got booted in favor of Jay Leno, was a topic of discussion.

Letterman was famously skipped over by NBC when Johnny Carson retired from "The Tonight Show" in 1992. Leno got the job and that damaged the relationship between the two late night hosts. It seems Leno's situation with O'Brien brought up some old feelings for Letterman.

When O'Brien first came out and sat down, he and Letterman didn't say anything to each other, but just smiled. Finally, Letterman blurted out, "I think the longer we just sit here, the more uncomfortable it will make Jay." O'Brien laughed, and said, "You know Jay's watching," and then, imitating Leno said, "Dave doesn't look happy … I think he's gonna pack it in, soon."

During the lengthy segment, Letterman said he's known Leno since the 1970s, when they were both young comics in L.A., and remembered Leno being "the funniest guy … the guy you always wished you could be." But Letterman quickly added, "He was also a bit of a brat."  Letterman told Conan that when the O'Brien/"Tonight Show" mess happened he thought to himself, "Oh, there's the Jay I know."

O'Brien stepped down as host of "The Tonight Show" in January 2010 and was soon replaced by Leno.  Letterman recalled relishing the criticism Leno got at the time from other comics who rallied to O'Brien's side. "I was delighted by everything that happened," Letterman told O'Brien, "except you losing your job … I refer to that period as the golden age of broadcasting."