Less than a month before he takes his final bow at the Ed Sullivan Theater, David Letterman has opened up to The New York Times in a rare interview.

The outgoing Late Show host talks about preparing for his final show, what will happen that night and what he'll do after that. He also shares his thoughts on the current late-night landscape, his memories of Johnny Carson, his rivalry with Jay Leno, his 2000 heart surgery and 2009 sex scandal.

Letterman says he's "awash in melancholia" and "full of trepidation" as he approaches his final show on May 20.

"Every big change in my life was full of trepidation," he explains. "When I left Indiana and moved to California. When [my wife] Regina and I decided to have a baby — enormous anxiety and trepidation. Those are the two biggest things in my life, and they worked out beyond my wildest dreams. I’m pretending the same thing will happen now. I’ll miss it, desperately. One of two things: There will be reasonable, adult acceptance of transition. Or I will turn to a life of crime."

In all seriousness, Letterman said he's decided "exactly" what he'll do on his final show there are still other things in the works not involving him. In terms of what that final show will be like, he says it won't be like Carson's goodbye.

"That was fantastic. I can remember when he signed off that night, it just left you [with] a nagging sense of loss. This doesn’t apply here," Letterman hints. "I want it to be a little more cheery. And I want it to be upbeat, and I want it to be funny, and I want people to be happy that they spent the time to watch it. Of course, Johnny’s last show was historic. This one won’t be. [laughs] This one, people will say: 'Ah, there you go. When’s the new guy starting?'"

He also understands how the late-night landscape is different than it was when he started, and he can't do what his younger competitors can.

"When I was watching those interim shows they did on The Late Late Show, and I saw John Mayer hosting one night, I thought, “Ohhhh, now I see exactly what the problem is,' " he explains. "Because he’s young. He’s handsome. He’s trim. He’s witty. He was comfortable. So then I realized, I got nothing to worry about. I know I can’t do what Jimmy Fallon’s doing. I know I can’t do what Jimmy Kimmel is doing. There’s nothing left to be worried about."

He adds that Leno leaving may have impacted his decision to bow out as he became the lone older man in late night.

"I’m 68. If I was 38, I’d probably still be wanting to do the show," he says. "When Jay was on, I felt like Jay and I are contemporaries. Every time he would get a show at 11:30, he would succeed smartly. And so I thought, This is still viable — an older guy in a suit. And then he left, and I suddenly was surrounded by the Jimmys."

Doing battle against the Jimmys for CBS will be left to former Comedy Central star Stephen Colbert, who was quickly named as Letterman's successor. Although Letterman seemed happy that Colbert would take over the show when the announcement was made last year, the outgoing Late Show host tells The Times that he wasn't consulted on the choice, something he was initially bothered by, but he's over it, aware that that's what happens when you decide to leave.

If he had been consulted, he might have brought up making a more diverse selection, he says.

"I always thought Jon Stewart would have been a good choice. And then Stephen. And then I thought, well, maybe this will be a good opportunity to put a black person on, and it would be a good opportunity to put a woman on," he says. "Because there are certainly a lot of very funny women that have television shows everywhere. So that would have made sense to me as well."

Letterman says he "will be completely in the hands of my family" after he signs off, for the first time able to plan his summer vacation around what his son wants to do.

But he speculates that leaving the Late Show might not mean saying goodbye to CBS, pointing out how Jane Pauley is now a CBS contributor.

"So maybe one day, something of that level will happen to me," he says.