How’s this for value? When Martin Short appeared on The Late Show with David Letterman one night this autumn, he gave of himself for more than 16 minutes—which, when you subtract the commercials and the monologue, accounted for the better part of the show. On the couch, he showered Letterman with unctuous faux flattery about the host’s youthfulness (“I was watching backstage. I thought, Is that one of the Winklevoss twins? They’re usually inseparable!”) and humility (“I love that you don’t thrust your Scientology at people!”). He did a couple of impressions, of Nathan Lane and of the show’s bandleader, Paul Shaffer. He came prepared with a good anecdote, about spotting his comic-actor friend Richard Kind from behind at a Washington party, wrapping his arms around Kind’s midsection, and buffoonishly declaring, “Oooh! Papa’s gained a little weight, hasn’t he?”—only to discover that the person he’d pressed himself against wasn’t Kind but David Axelrod, Barack Obama’s chief campaign strategist.

And then, to cap it off, Short offered, literally, a song-and-dance routine. First, he announced that he had reconciled with his brothers, Manny and Morty, with whom he had fallen out after a successful touring career in the 60s and 70s. And then, with fanfare, he introduced the re-united Short Brothers: himself plus two black singer-actors. The three of them went on to harmonize on a pre-election ditty about undecided voters (It’s either Rom-ney or O-bama / One built Bain; one killed O-sama), its verses punctuated by outbursts of spasmodic tap dancing by Short that recalled the most famous of his sketch-comedy characters, the touched but cheery man-child Ed Grimley.

Marty Short, all five feet seven of him, gives good talk show. As Shaffer explained after the Late Show taping, “A guy like David Letterman is so happy when Marty’s on, because he knows he can relax. He knows that Marty will take care of it—that he’s going to give you a couple of segments of socko.”

Short does this with regularity—not only for Letterman but also for Fallon, Conan, Kimmel, and Ellen. There used to be more like him: a whole talk-show ecosystem of Dinos, Sammys, Grouchos, Milties, and Toties who bounded onto soundstages in Midtown and Burbank and just delivered, entertaining for entertainment’s sake, unhampered by sulky-actor social ineptitude or a studio-mandated obligation to plug something. (Though Short threw in some plugging on Letterman, too, dutifully devoting a sliver of time to his voice work for Tim Burton’s Frankenweenie.)

Nowadays, however, there’s really no one else out there like Marty. And while his shtick undoubtedly comes with an overlay of winking commentary on the tired conventions of show business—witness his evocation of the old-time vocal group the Mills Brothers in the Short Brothers bit, or his customary shouted greeting to Letterman’s studio audience every time he visits, “Thanks for remembering!”—Short is genuine in his desire to entertain: an authentic trouper beneath the pretend inauthenticity.

Above all, Short is very funny. He can be funny in the neo-vaudevillian way of his talk-show appearances and Broadway performances (in such productions as his 2006 revue, Martin Short: Fame Becomes Me, and the 1998 revival of Neil Simon’s Little Me, for which he won a Tony), and he can be funny in the profoundly odd, sui generis Martin Short way he was on SCTV, Saturday Night Live, and Primetime Glick, where he went deep into deranged character—whether as Grimley, or the albino lounge singer Jackie Rogers Jr., or the clammy corporate-shill attorney Nathan Thurm, or the goitered, vapid celebrity interviewer Jiminy Glick—with full commitment and nary a knowing wink to the crowd.