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Except for a sly, slightly gap-toothed grin, David Letterman looks sane, all right, six feet, two inches of Midwestern reserve in a sensible coat and tie. But when he ambles onto the New York City skyline set of his Late Night talk show, askewness looms. Odd-lot ordinary citizens introduce pet worms or parrots dressed as boxing promoter Don King, and Dave greets them with the gee-whiz enthusiasm of a 4-H club judge evaluating prize sorghum. Okay, the guy is from Indiana. But then he consents to being covered with tortilla chips and gradually lowered into a vat of onion dip and you have to wonder....

Whatever Letterman has, it's catching, and it's clear his celebrity guests are not immune. How else can you explain Tom Selleck sticking his head into a galvanized washtub and impersonating a motorboat? Or Mariel Hemingway gutting catch o' the day on Audience Fish Cleaning Night? Or Cybill Shepherd appearing in a towel? Or Connie Chung crushing walnuts with her bare hands? Or Ted Koppel balancing a dog biscuit on his distinguished newscaster's nose? These are clearly the desperate acts of men and women who have played straight too long, who look for leadership to the kind of man who would dress up in a suit of Velcro, catapult off a trampoline and stick, spread-eagled, to a corresponding Velcro wall—which Letterman once did. "On this show I know I'm not going to be treated with the respect due my position," jokes Today show co-anchor Jane Pauley. "Most likely I'm going to be embarrassed within an inch of my life."

With promises like that, it's no wonder that 3.7 million fans—half of them between 18 and 34—tune in nightly to Letterman's inspired lunacy. The 39-year-old former funny weatherman is a hot property, courted for the Emmys (which he's co-hosting in September) and touted as a successor to Johnny Carson. NBC's Late Night With David Letterman may be the hippest show on network television. "They used to call us a cult favorite," he says. "I thought that meant 'nobody's watching.' "

In a genre that is usually as spontaneous as microsurgery, Letterman seeks unpredictability. "When a guest is being strange," he says with relish, "I have the feeling that I'm watching a live grenade being rolled into a restaurant at brunch. Most TV is totally unsurprising. On our show we want viewers at home to look at each other and say, 'What the hell was that?' We want to pierce that flat TV screen."

Jolting the viewer means cutting back on that talk show staple: stars with something to sell. "We're not too interested in being the 11th talk show to have Joan Collins talk about character development," Letterman explains. Collins, understandably, has not ventured onto Late Night. But Letterman asked model Cheryl Tiegs if she really wore those Sears clothes that she endorsed ("Yes," she said). And instead of promoting Rambo: First Blood Part II, actress Julia Nickson found herself telling the world that co-star Sylvester Stallone shaved his arms. Now, she says, jokingly, "Sly doesn't speak to me."

Some celebs, accustomed to marsh-mallow interviews in which they set the guidelines, find Letterman's guest chair too hot. ("Sometimes Mr. Letterman's honest interviews insult my clients, and then they blame me," says one publicist.) But if the guest is game, the result can be revealing. Pauley, for example, played along enthusiastically when an audio trick made it appear that she was under the influence of laughing gas. Most celebs say they enjoy letting their hair down. "I get nervous talking about myself for 10 minutes on a talk show," explains Selleck. "But Letterman gives me the opportunity to make an idiot of myself."

The best guests, according to Late Night producer Barry Sand, are those who "understand the show and come ready to play." When Cybill Shepherd's dress arrived at the studio a week before her scheduled visit, Letterman used it as a promo device. Not to be outdone, Shepherd, when she arrived, ignored the dress and came on in a towel. "It seemed appropriate," says the Moonlighting fashion plate. "Most talk show hosts only want to score points at the guest's expense, but David's humor comes from the situation." Even the grand old man of talk, Johnny Carson, got into the spirit. When he guested with Letterman, Carson brought along his own collapsible host's desk. When he had Letterman on The Tonight Show, Carson aired a clip showing Dave's beat-up pickup truck being towed from Letterman's 5 second home in Malibu—a joke Johnny had arranged. "He takes an irreverent look at the world," says Carson. "I just wanted to surprise him."

Although some talk show hosts make it perfectly clear that they don't like being upstaged, Letterman swears that his favorite guests are people who out-outrageous him. "I want a guest to come in and derail me," he says. "Sometimes when I swarm a person, it's only because it's not going the way I hoped, and my instinct is to try to make it funny." One of his preferred frequent flyers is comedian Jay Leno, who comes prepared with routines like What's My Beef? Another favorite is actress Teri Garr, who plays a dizzy Gracie Allen to Letterman's George Burns. Garr delights Letterman because, he says, "Half the time I'm apologizing to Teri for what I did to her last time." Perhaps regretting that he had persuaded Garr to take an on-camera shower in his office ("In retrospect, it looked like a VFW smoker"), Letterman sent her an electronic bouquet: Teri Garr Week, four nights of reruns on which she had appeared. "David is 'mean' like my brother was," says Garr, who takes Letterman's kidding in stride. "That's not really mean."

A handful of those who have been lampooned by Letterman would disagree. Actress Nastassja Kinski reportedly was miffed that Letterman teased her about a hairdo that laughed at gravity. Bryant Gumbel was not amused when Letterman interrupted an outdoor Today show special in Rockefeller Center, shouting from his own taping sesssion above, "I am Larry Grossman, President of NBC News...and I'm not wearing pants!" ("I don't blame Bryant for being pissed, but we were invited in by the Today show producer," says Letterman. Unfortunately, nobody told Gumbel and Pauley.) And Entertainment Tonight co-host Mary Hart was no match for Letterman when she went on the show after he repeatedly labeled her "damned perky." Notes Don King, a Letterman fan, "You have to parry with him. But if you get into a repartee game, he's gonna win." Still, it should be noted that Letterman frequently shows great restraint with easy marks. "I was warned he was a tiger," says Eva Gabor, "but he's a pussycat."

An unexpectedly shy, sobersided man, Letterman is sensitive to the charge that he occasionally goes too far. "I feel very uncomfortable asking personal questions because I wouldn't want to answer them myself," he says. "But how can you have Bianca Jagger on the show and not ask her about Mick Jagger?" (After posing the question, Letterman laughed nervously and Bianca pronounced him "much nicer than I expected.") Observes Letter-man talent coordinator Sandra Furton, "David worries about asking personal questions."

Who gets to Letterman? Cher. When she appeared on the show for the first time in May, Letterman asked her why she'd been reluctant to be a guest. Cher replied, with a straight face, that she thought he was an "asshole." The audience roared, but Letterman was discombobulated and never recovered for the rest of the evening, even though Cher slipped him a note that read, "Dearest David, you're not an asshole, love, Cher." "It did hurt my feelings," Letterman admits. "Cher was one of the few people I've really wanted to have on the show, and then she calls me an asshole. I felt like a total fool, especially since I say all kinds of things to people. I was sitting there thinking, 'Okay, Mr. Big Shot, can you take it as well as you can dish it out?' "

It is 7 p.m. at Late Night Central, a rabbit warren of offices within NBC's Manhattan headquarters. After taping the show before an adoring young studio audience at 5:30 p.m., the host repairs to his modest executive digs, which are unremarkable except for the pile of athletic equipment(he's a baseball nut and jogs five miles a day) and the 30 pencils stuck into the ceiling directly above his desk. Changing into a football jersey, shorts and a silly-looking golf hat, he muses on that weird job description, talk show host. "When I was growing up in Indianapolis, my parents, who regarded TV as the work of Satan, told me to go outside and do something real," recalls Letterman, whose late father was a florist. Naturally, "I always wanted to be in radio or television. I had to be a talk show host—I can't sing or act."

The format of Late Night—which is really a comedy show more than a talk show—goes back at least as far as Letterman's oddball daytime show on NBC in 1980. "Some of the stuff we're doing on this show we first tried on the daytime program," he says. The difference was that the daytime watchers didn't cotton to the antics of such guests as guerilla comedian Andy Kaufman, who once panhandled the studio audience. Letterman won two Emmys, but the show was canceled after 18 weeks. "I made life pretty miserable for my girlfriend," says Letterman, who then and now lives with writer Merrill Markoe, 38. "I thought that was my one shot."

Before he found the niche for his observational humor on Late Night, which premiered in 1982, Letterman had been a TV talent waiting to happen. After graduating in 1970 from Indiana's Ball State University, where he was a campus disc jockey who majored in puns, he worked as an announcer and wiseacre weatherman in Indianapolis. His offbeat stand-up routines at the Comedy Store in Los Angeles, where he moved in 1975, led to a regular spot on Mary Tyler Moore's ill-fated variety show Mary in 1978. He guest-hosted Tonight many times, and NBC signed him to an exclusive contract. Letterman—who makes more than $1 million a year—says he has no designs on Carson's job. "After 24 years Johnny is the home-run king in this business," he says. "There's no way I'd want to compete with his record."

Like Carson, Letterman avoids a public life-style. "David is never 'onstage' even when he's onstage," notes his friend Jay Leno. Although several of the celebrities interviewed by PEOPLE spontaneously offered the wish to have Letterman as a friend, he rarely hangs out with famous people. His best friends are his devoted staff of writers, with whom he likes to attend baseball games. When the show is over, he usually splits for a home in Connecticut, which he shares with Markoe. "We're the two worst social people ever," Markoe has said. "This is not life in the fast lane." The couple met in 1977 at the Comedy Store, where she was testing her own material. The head writer on Late Night until its second season, when she started pursuing her own projects, Markoe is the one who invented Stupid Pet Tricks and other Late Night legends. "She's funnier than I am," Letterman says seriously.

All these questions about his guests have got Letterman thinking about what makes him blush. "Dr. Ruth Westheimer does embarrass me with all her talk of clitorises and penises," he says, blushing.

Aha—so what we have here is an Indiana boy, wryly observing the "found" humor in such real-life events as National Soup Month—and gently tweaking the pretenses of celebrity. "I'm just trying to make a smudge on the collective unconscious," he says.

Since celebs don't get the last word on Letterman, let's let one have the last word on Letterman. Take it away, Dr. Ruth: "He stumbles every time he has to say the word orgasm," she says. "But he's getting better."