Associated Press
Actress Jennifer Lopez talks with David Letterman during an appearance on "Late Show with David Letterman." Letterman is celebrating 30 years in post-prime-time television.

LOS ANGELES — David Letterman celebrates 30 years in post-prime-time television this week, spent first as the host of "Late Night With David Letterman" on NBC and then, since 1993, of "Late Show With David Letterman" on CBS.

He went to CBS, famously, after NBC gave "The Tonight Show" to Jay Leno, despite an endorsement for Letterman from its departing host, Johnny Carson (who in his retirement would also sometimes supply him with jokes). It was a bitter pill that still produces the odd quip from Letterman, nearly two decades later.

Carson's "The Tonight Show" was an institution — Leno's, not so much — but it wasn't a bad thing for Letterman to lose that war. The underdog status suits him; it allows him to position himself as an outsider, in show business but not exactly of it. (I speak relatively, of course, of a man whose 2011 earnings, from show business, Forbes estimates at $45 million, but every dog has his context.)

Leno, his time-slot competitor, reliably draws more viewers, but Letterman has created a community, partly from having remained in New York: Right outside the theater doors, mad, bad, beleaguered and attacked, the city reflects "Late Show" as "Late Show" seems to speak for it.

The self-deprecation is, of course, also a kind of misdirection (and an inheritance from Carson, who perfected the art of getting a laugh on the back of an unfunny gag). Letterman is one of the great figures of television; It is his natural medium, both in the sense of an art he practices and the element in which he swims. He rules his turf; there is no desperation in his presentation; he does not need to impress you or the celebrities who sit next to him.

As the king of all he surveys, he can afford to be himself; he is comfortable enough to be seen as uncomfortable — to actually be uncomfortable — though even his worst real-life moments and most sincere apologies for misfiring jokes have a way of fueling more jokes. He controls the field in a way that leaves room for accidents and integrates them into the comedy.

Letterman turns 65 this year; it has been a dozen years since he underwent a quintuple bypass, and he looks fit, if grayer and balder. But except to downplay his intelligence, he doesn't pretend to be other than he is. ("When I was your age I had a paper route," he told Lady Gaga recently.)

Letterman is a private person, but he is also a present one; you feel that what he offers you, from himself, from his show, if it does not amount to Total Disclosure is nevertheless something authentic, or at least more authentic than it needs to be. Like Carson's, his program is more party than sales pitch. Stars come to hawk their wares, of course, but there is also an acknowledgment of that process and bargain.

Like Craig Ferguson, whose post-"Late Show" "Late Late Show" Letterman's Worldwide Pants produces and who showily rips up his note cards before each interview, he is more of a conversationalist than a prompter; he is liable to follow his own interests and leave the promotion nearly alone. Guests come to him on his terms; when they don't, as in Madonna's 1994 attempt to hijack the show, or Joaquin Phoenix's performance-art appearance in 2010 ("Joaquin, I'm sorry you couldn't be here tonight," Letterman said finally), they don't win.

If he has a politician on, he will (usually) ask questions of substance. "A lot of guests, world leaders in particular," he told Tony Blair, "are here once and don't come back." When nominee John McCain, tiring of questions about his choice of Sarah Palin as a running mate, asked, "Have we pretty well exhausted this topic?" Letterman replied, "No, no. I'm just getting started."

The memorable television "Late Night" and "Late Show" have provided has not always been predicated on good times: There was his first night back after 9/11 ("If you live to be a thousand years old, will that make any sense to you?") and the revelation in 2009 of a blackmail attempt over affairs he had with employees and interns, and the apologies to his staff and to his wife (which put an unpleasant collateral spin on his habit of going on about the loveliness of many female guests).

An Islamist online call for his death last year produced some good lines: "Tonight, you people are ... more than an audience — you're more like a human shield" and "This seems like Leno's handiwork." And the hour he spent in 2002 with the terminally ill Warren Zevon, a friend of the show and sometime fill-in bandleader, was deeply felt, without their forgetting to be funny.

Thirty is also the number of years that Johnny Carson hosted "The Tonight Show." Letterman has made "Late Show" an institution itself; he is the late-night figure younger comics look toward the way his generation looked toward Carson. Bill Murray, the first guest on both of Letterman's late-night shows, was his guest again Tuesday night, on the eve of his anniversary.

As he produced a cupcake and candles for the host to blow out, Murray summed him up nicely: "Dave doesn't like to make a big thing about himself, the fact that his name is on the marquee out on Broadway notwithstanding."

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Wednesday on TV

Person to Person (7 p.m., Ch. 2): Actor George Clooney; businessman Warren Buffett; musician Jon Bon Jovi.

Nature (7 p.m., Ch. 7): Scientists follow a family of urban raccoons.

American Idol (7 p.m., Ch. 13): Vocalists compete for a spot in the semifinals.

Criminal Minds (8 p.m., Ch. 2): The team investigates ritualistic casino-related murders.

Modern Family (8 p.m., Ch. 4): Claire thinks Phil's new business partner is blatantly inappropriate.

NOVA (8 p.m., Ch. 7): Conjoined twin girls undergo a series of delicate operations.

Mobbed (8 p.m., Ch. 13): Howie and choreographers stage a dance audition for a 37-year-old man who will do anything for a chance to meet his father.

CSI (9 p.m., Ch. 2): A woman dressed in vintage clothing and sporting a hairstyle from the 1970s is found dead.

Law & Order: SVU (9 p.m., Ch. 5): A woman is found in Central Park unconscious.

Inside Nature's Giants (9 p.m., Ch. 7): Dissecting a lion and tiger.