What makes for a good chat-show host? You'd have thought perfect teeth were a prerequisite, but David Letterman is the exception that proves the rule.
He has a great big whistling gap in his, but a few weeks back he celebrated 30 years as a talk-show host, a milestone only equalled by his hero and mentor, Johnny Carson.
In the US, where you're only a bad season's ratings away from oblivion, this is a significant achievement, but Letterman was doing his best to avoid acknowledging it.
He refused interviews, made a few throwaway jokes about the anniversary on his show and briefly shared memories with his longtime bandleader, Paul Shaffer. But that was as far as it went.
Letterman's reluctance to make a fuss may have something to do with the fact that he's still recovering from the embarrassing events of October 2009, when a botched attempt to blackmail the presenter led to revelations about his multiple affairs with female subordinates stretching back decades.
He made a profuse public apology and rode out the media storm.
At the time, some even wondered if his long-running chat-show career might come to an end, but it turns out the American public don't really care what he's doing or to whom he's doing it, so attached are they to his bawdy, sarcastic interviewing style.
It now looks like Letterman will sign a two-year extension to his contract at CBS that will make him the longest-serving American chat show host ever.
So what is it that makes David Letterman so good at his job, despite some obvious disadvantages? The answer seems to be quick wits, and a bombastic personality that's made him as big a star as most of his guests.
In America, Letterman and his great west-coast rival Jay Leno are as instantly recognisable as movie stars, though without the looks.
Leno is portly, and Letterman breaks the golden rule of American showbiz -- he has crooked teeth.
In fact, he breaks a lot of rules, and he became popular in the 1980s because of his tendency to poke fun at the whole talk-show format.
He threw his pen at the camera, kicked back and put his feet on the desk and elicited the studio audience's sympathy whenever a guest was being truculent.
He almost seemed to be laughing at the very idea of celebrity interviews, but Hollywood queued up to appear on his late-night show, and the sarcastic maverick became an institution.
But Letterman was not being quite so revolutionary as it might appear , because a good deal of his style had been honed while appearing as a guest on Johnny Carson's 'Tonight Show'.
Letterman himself has admitted he owes a lot to Carson, who in many ways is the prototype of the modern chat-show host.
Carson is the man who proved that a chat show is only as good as its host. Before him, NBC's 'The Tonight Show', which launched in 1954, had been hosted by Steve Allen and Jack Parr and ran late-night for almost two hours.
Allen and Parr had their moments, but Carson made it all seem much easier. When he took over in 1962, he pulled its length back first to 90 minutes, than an hour.
He introduced his own house band, opened the show with a monologue peppered with up to 20 jokes, and appeared in skits and sketches during the show.
His on-camera style was relaxed: he joked with guests and had a talent for making them feel at ease. But his show was brutally efficient. If a guest was bombing, they'd go to a commercial and get rid of them.
Carson was ruthless, but America loved him. His slick, finger-clicking style made him the biggest thing on US television in the 1970s and 1980s, and there was a national outcry in 1992 when he retired.
Everyone from Letterman and Leno to Oprah, Ellen DeGeneres and Conan O'Brien still cite him as an influence.
For all his ratings success, however, Carson's interviews tended to be quick, glib and superficial, but in 1970s Britain, another kind of talk-show style emerged.
Michael Parkinson was a former newspaper reporter from Yorkshire who drifted into television in the early 1960s and landed his own talk show on the BBC in 1971.
Parkinson's bluff good humour and quintessential blandness set him at odds with the likes of Carson, but 'Parky' had a way of getting to his guests and lulling them into a false sense of security.
Watching his show was like watching a clever angler: he would butter up the likes of Bing Crosby and Orson Welles before reeling them in and getting them to reveal far more than they'd intended.
Parkinson interviewed practically everyone who mattered in the 1970s and early 1980s, and got more out of notoriously difficult interviewees like Muhammad Ali and Peter Sellers than anyone else did.
In Ireland, Gay Byrne was performing perhaps an even more difficult trick. 'The Late Late Show' required him to move from political interviews and social traumas and debates to fluffy celebrity interviews in the same two-hour show every Friday night.
Just how good he was at doing this only became evident after he retired in 1999 -- he's proved a hard act to follow, and is still the longest-serving chat-show host of the lot.
Byrne succeeded by establishing an easy intimacy with his audience, who ended up thinking of him as some sort of close relative.
This was perhaps easier in a country this size, but, over in Britain, Terry Wogan managed to do something similar with a much larger audience.
In these edgy times, however, the talk-show style has changed. Wogan was a big influence on Jonathan Ross, but Ross played the buffoon more broadly and coarsely and also made himself the centre of attention on his very successful BBC show.
He recently moved to ITV, and has just signed a two-year deal, but the common consensus is that he's being trounced by his replacement at the BBC, Graham Norton.
Norton added half a million viewers to Ross's Friday-night slot on his first show in 2010, and seems to be attracting more of the big names than Ross's ITV show as well.
Norton treads a fine line between skittish good humour and lewd subversion, and effortlessly manages to orchestrate free- flowing conversations with three guests at once. He's even been described as 'the 21st century's answer to Terry Wogan', but Sir Terry was a lot less edgy than him.
He might not be as bombastic as talk show hosts such as David Letterman, but Norton gets away with a whole lot more.