Want to win the Kennedy Center’s Mark Twain Prize for American Humor, arguably the laughter industry’s most prestigious annual award?

It’ll help your chances if you’re actually funny, which is a key reason Carol Burnett was named the 16th recipient of the prize on Tuesday. But other factors influence the tight circle of Kennedy Center insiders who make the selection each year.

Would-be winners need to be famous enough to draw a large audience to a PBS telecast of the prize ceremony in the fall. They also have to be popular enough to draw corporate sponsors to a pre-show “rehearsal” dinner in their honor and to sell tickets to the ceremony itself (all of which raises about $1 million a year for the Kennedy Center).

Other requirements: a posse of famous friends willing to roast and toast the recipient on the air. And a desire to get the thing in the first place: Bill Cosby twice turned down the prize because he was offended by the foul language during the inaugural presentation to Richard Pryor in 1998. (Cosby relented and accepted in 2009.)

Because of the TV ceremony’s visual imperatives, it pays to have spent your career in movies and television, with a long trail of TV-ready clips (Mark Twain, who did his best work in print, would have a hard time here). Only one writer, Neil Simon in 2006, has ever been selected. Garrison Keillor — a radio humorist who has occasionally been compared to Twain — probably doesn’t stand a chance.

Oddly, the Kennedy Center’s spokespeople won’t say who actually selects the winner or what criteria it considers. Repeated inquiries elicited only a vague and not terribly funny response: a committee. “A short list is compiled by the executive producers [of the ceremony] and presented to a group comprised of representatives from the Kennedy Center board of trustees, as well as the Kennedy Center senior management and programming staff,” said Amanda Hunter, a spokeswoman.

As Jerry Seinfeld might say, who are these people? The Kennedy Center’s staff declined to name names, deferring questions to Cappy McGarr, a Kennedy Center board member who is the co-founder and co-executive producer of the Twain Prize.

In fact, McGarr said in an interview Monday, “there’s really no committee.” Instead, he said, the award’s executive producers — McGarr, Mark Krantz and Peter and Bob Kaminsky — have always decided in consultation with the Kennedy Center’s chairman and president, David Rubenstein and Michael Kaiser, respectively. “It’s really a consensus decision,” he said. “There’s not any single person who decides.”

The primary criteria: “We try to choose people who’ve had a full lifetime of making us laugh and who’ve had a great influence on the people who’ve followed them,” he said. “I don’t think being famous has anything to do with it. I’m not sure how many people know who Neil Simon is. But they know ‘The Odd Couple.’ They don’t know Lorne Michaels [the 2004 winner]. But comics do.”

While none of the deciders is in the comedy business — McGarr and Rubenstein are investment bankers; Peter Kaminsky is a food writer and cookbook author, for example — McGarr says that’s not really an issue. “We get an incredible amount of input from the comedy community,” and the public, he said. “After 16 years of doing this, we’re all pretty tuned into the comedy world.”

Indeed, agents and publicists helpfully inform the producers that their clients are available to receive the prize.

For most of its existence, the prize was bestowed upon a comic immortal, turning it into a de facto lifetime achievement award. The winners included septugenarians such as Jonathan Winters (73 when he was named in 1999), Carl Reiner (78 in 2000), Bob Newhart (72 in 2002), Simon (78) and Cosby (71).

George Carlin, the winner in 2008, satisfied the requirement that recipients be living, but just barely. He died at 71 just four days after being notified he had been chosen. The show went on without him that fall.

At 80, Burnett is the oldest recipient ever. Her selection reverses the trendlet of recent years, in which younger performers in the middle of their careers were recognized. Tina Fey, the 2010 winner, was the youngest winner, just 40, and a relative newcomer, with barely a decade in the national spotlight. She was followed by Will Ferrell (then 43) and Ellen DeGeneres (54).

Apart from the occasional debate about an overlooked legend — Woody Allen? Mel Brooks? Joan Rivers? — the Twain Prize has generally avoided the kind of selection controversy that has beset the Kennedy Center Honors. Latino groups had been critical of the Honors for underrepresenting performers of Hispanic heritage. The protests led the Kennedy Center to announce last week that it is broadening its selection process, with the creation of a Latino Advisory Committee, among other changes.

Some conservatives grumbled about the selection of Fey, DeGeneres and Ferrell, suggesting they were chosen as much for their political sympathies as their comedy (Fey is famous for her withering parody of Sarah Palin; Ferrell co-wrote and performed a one-man Broadway show that savaged President George W. Bush; DeGeneres is one of Hollywood’s most famous lesbians.)

But McGarr dismisses such commentary. “Unequivocally, this has nothing to do with politics,” he said. “It has nothing to do with anything other than being funny.”

Comedy blogger Todd Jackson doesn’t quibble with any of the Twain selections, but he does raise another question: Should comics and satirists — the ultimate outsiders — be embraced by the very establishment they’re supposed to be ridiculing?

“Jerry Seinfeld once won a comedy award and said, ‘I feel like I should be in the back of the room making fun of this thing,’ ” said Jackson, whose all-comedy site is called Dead-Frog.com. “That’s how I feel about this. The whole point of being a comedian is, if you’re not pissing someone off, you’re not doing your job.”