Williams is a regular on both shows, which means he sometimes has to deal with the awkward fact that Leno, his fellow NBC host, is a bitter rival of Letterman’s. On Monday’s show, Letterman seemed determined not to let him forget it.

“I don’t like it when you go on that show,” he said.

“That’s funny, because he doesn’t like it when I come here,” Williams replied.

“Could you not go on that show?” Letterman persisted. He also dropped into an impersonation of Leno, pointed out that it takes much less time for Williams to travel to his studio in Midtown Manhattan than to Leno’s studio in Los Angeles, and mocked the idea that Leno is a blue-collar guy (“He’s got 400 cars,” he noted).