In a recent conversation with Vulture’s great interviewer David Marchese, the actor and comedian Martin Short talked a bit about the process he goes through when preparing to be a guest on a late-night talk show. “What I do for a typical talk-show appearance, and I’m not exaggerating, is I’ll send in something like 18 pages ahead of time,” Short said, adding that he then spends at least ninety minutes speaking with a show’s producer, cutting down his proposed material and shaping it into a conversation he’ll have with the host. What looks almost like an organic chat on TV is really a tightly choreographed two-man bit, with Short doing, as he puts it, “an impersonation of myself being relaxed.”

He’s not alone in preparing meticulously. During his last appearance on the “Late Show with David Letterman,” in 2015, Short told a story about how his friend Steve Martin would call him, from time to time, to tell him a joke that he was readying for a “Letterman” appearance that was still months away. (And less fastidious guests are compelled by most late-night shows to at least have their material vetted before they appear.) Yet one gets the sense that, of all his peers, Short is the hardest-working talk-show guest in the business—and, as a result, he may also be the greatest. He has starred in movies, sitcoms, variety shows, and stage performances, and he even, for a season, hosted his own talk show. He’s won Emmys and a Tony and nearly every award that Canada gives out. Yet, despite his wide success, some of his greatest comedic triumphs have come while yakking with talk-show hosts.

YouTube is full of Short’s talk-show appearances, dating back to his first spot on “Letterman,” in 1982, and regularly I find that I’ve killed half an hour or so watching his old clips. Short, who is now sixty-seven, has always been tirelessly boyish and energetic, and has made several generations of hosts lean back in their chairs and laugh. He cracked up Carson. He’s cracked up Leno. And Conan. And Fallon. He’s funny anywhere, even in places where laughter is hard-won, like on “Regis and Kelly” or Chevy Chase’s short-lived talk show. He’s even funny when he’s hiking. Of all the truly great modern talk-show guests—a list that includes Amy Sedaris, Norm Macdonald, and just a handful of others—it is Short whose clips I return to time and again. Mostly, I think, it’s because his talk-show persona is the purest, the most attuned to and at ease with the restrictions and comedic traditions of the genre. Nobody tells a vacation story, or a holiday story, or an awards-show story, or a recollection of some industry folly better than Short does. He sings; he dances; he does broad physical comedy; he tells the best one-liners.

Short has always understood that being a talk-show guest is itself a performance, a role to cultivate and refine. The persona he has settled into is that of a self-assured but ever so slightly bitter show-business insider, a breezy phony, a Hollywood jerk. He walks onstage wearing a little smirk, and then makes a show of basking in the applause of the audience. He repeatedly refers to the “Daytime Oscars” he’s won, and makes passive-aggressive jokes about the fact that the show didn’t send a car for him, or about the cash bars that his rich Hollywood friends have at their parties. Sometimes he channels the louche vibe of a lesser Rat Packer. Other times, he drifts off into a Norma Desmond, faded-grande-dame kind of thing. He often seems to be doing two or three impressions at once. He likes to open his appearances with a series of rim-shot jokes made at the expense of the host, in the style of Don Rickles. “You look sensational,” he tells Letterman. “Is it the kale enemas?” To Jimmy Kimmel: “Every time I’m in your company, I’m whelmed.” To Conan O’Brien: “You look like the film negative of ‘Django Unchained.’ ” To Jimmy Fallon: “I bet you’re the only late-night host that goes to a pediatrician.” The jokes, rehearsed and not always original, nonetheless always kill, and they provoke glee from the hosts, who take obvious delight in being roasted by Marty, as they all call him.

Short’s bluster is tempered by what, one senses, is his realer personality, characterized by Canadian self-deprecation and downright decency. In 2012, during Short’s appearance on the boozy fourth hour of the “Today” show, the host Kathie Lee Gifford asked Short how he and his wife, Nancy Dolman, kept the spark alive in their marriage, and went on to ask several more questions referring to Dolman in the present tense—unaware that she had died of ovarian cancer, two years earlier. Short appeared briefly taken aback, but managed to smile while answering the questions as best he could—waiting to correct Gifford until they were off the air.

Nowhere was Short in better form than in his fifty-plus appearances on “Letterman.” This owed, in part, to his longtime relationship with Letterman’s bandleader, his fellow-Canadian Paul Shaffer, whom he would relentlessly tease. (“Paul looks like the maître d’ on a spaceship.”) But mostly his Letterman appearances thrill because he so clearly has the number of the host, a notoriously hard nut to crack. Short makes Letterman laugh—really laugh, that great cackle—and this endorsement spurs the audience to even greater laughter. The talk-show guest is, in a way, a supplicant—seated lower than the host, with just a few minutes, between commercial breaks, to make a good impression and plug whatever he came to plug. It’s a frankly ridiculous situation, and faintly demeaning—a dynamic that Short at once embraces and mocks. Being a guest suits his seeming need to impress, to relentlessly wear down an audience, to paw at a person sitting a few feet away until he forces a laugh. Short is endlessly charming, but the characters he plays are often pests or interlopers, grating and bizarre, and this friction, packed into a few minutes, yields a perfect whirlwind of knowing wit and wild abandon.

The last thing Short ever did on “Letterman” was sing a song. With his body arched back and his legs spread wide, he belted out, “It’s the end, my pretend show-biz friend, farewell! We’ll meet again, someday, in hell.” Short told the audience that he had planned to deliver the number as a eulogy at Letterman’s funeral. But since Letterman was quitting television, he added, he probably wouldn’t show up when Dave actually died—“unless, of course, I have something to promote.”