When he accepted the March 1995 gig, Letterman was on top of the world. He had defected to CBS after NBC chose Jay Leno as Johnny Carson’s successor on “The Tonight Show,” and “Late Show With David Letterman” was beating Leno handily in the ratings. When the ABC president Ted Harbert announced Letterman’s selection as Oscars host, he said hopefully, “If Dave likes the experience, this could be a great answer for the show, just the way Carson did the show for many years.”

Carson was Letterman’s hero, and stepping into his shoes (particularly after being denied Carson’s desk) was certainly a factor in accepting the Oscars job. But there was more to it, Letterman told me: “It was ‘pride goeth before the fall.’” This was something he was expected to do, at the level of success he had achieved. “I have no choice. I have to do this,” he remembered thinking, adding, “I cannot now say no.”

From the beginning, Letterman and his longtime producer, Rob Burnett, determined that the smartest strategy was to do what they did best, “things that had proven successful for a number of years.” So they peppered the ceremony with favorites from Letterman’s late-night shows: a monologue, a Top 10 list, wry taped segments, even a Stupid Pet Trick.

But for all the preparation, Letterman was also open to inspiration. “Rob Burnett, who was very good at last-minute things, he says to me — literally with 20 minutes to go — he says, you know what you can do? You go out and you say, ‘Oprah, Uma? Have you met Keanu?’ And I said, that’s genius. That is genius. I’m there.”

It was the kind of thing Letterman did on his talk shows all the time — seizing on a funny turn of phrase, overselling it, then using it as a silly running gag, an oddball refrain to fill awkward pauses.