Wearing only a slip and high heels, Babette, a French sex kitten, found her song interrupted when police raided the late-night Chicago club at which she was singing. No, this was not a scene out of The Untouchables. The comic chanteuse was really Saturday Night Live's Nora Dunn, but the police bust was no act—the club didn't have a liquor license. "It was a classic," Dunn says of the 1985, pre-SNL incident. "I peeled out the back door and down the alley in just my slip. This guy I was dating had come to see the show, and as we're running down the alley, he says, 'Boy, you sure know how to show a guy a good time!' "

Dunn, 35, has been on a run ever since. Soon after, she auditioned for SNL and now gets to show millions a good time with her array of caustically funny characters, including Babette. Dunn is best known as the vacuous talk show host Pat Stevens, prone to such pronouncements as, "I know there's famine, war, disease and other bad things in the world, but I love shoes."

Ratings for last year's show were the best since 1981. And the entire cast is back this season, including Dana Carvey's Church Lady, Jon Lovitz's liar and Dennis Miller's Weekend Update anchor. The pressures of doing a weekly show are enormous. "There is competition," she admits, "but it's not back-stabbing." Now, in her third season, Dunn finds the show much easier on her nerves. "I don't live and die for the show every week like I used to," she says. "I still feel very intense and care a lot, but the show is not the most important thing in the world."

Sadly, it took the death of her father, musician John Dunn, for Nora to come to that realization. "I was so immersed in my career, I think I might have ignored other things—like relationships," she says. Her dad never missed an SNL show; he even watched the night before he died of cancer in March 1986. But Nora was too busy with her career to spend time at home with him or to see his pride in her work. After the funeral, she was going through his papers and found something that brought tears: Her father had kept a scrapbook of her press clippings.

Dunn insists she won't let her career cut her off from her husband of two months, Ray (Duck Blind) Hutcherson, 38, a Chicago playwright. It's the first marriage for both. "I have a life now," Dunn says happily. The pair married in September and honeymooned at a friend's turn-of-the-century cabin on a river in Wisconsin. They met three years ago in Chicago when one of Hutcherson's buddies, who used to date Dunn in high school, insisted that Ray see her perform. Hutcherson recalls his reaction: "I thought, 'I'm going to meet that woman if it takes all night.' "

Dunn says she avoided Ray for weeks, fearing he'd expect her to be the same funny person that she is onstage. "No one is as interesting as their work," she says. "But his apartment was about three blocks from mine, and I think he would create these coincidences to run into me." Hutcherson lets out a big laugh and says Dunn would watch his apartment. They both agree that they started dating after having a great chance meeting at the Northside Cafe. Who ran into whom is still an open debate.

There is no debate, however, about the strength of their relationship. "We just have the same idea about the kind of work we want to do," says Dunn.

And she adds, "He's also quite handsome." Says Hutcherson admiringly: "Nora is quality. Her whole family is grounded in this decency."

One of six children, Nora was born in Chicago and raised in a rough neighborhood. "We were sort of isolated, so we became real close," she says of her siblings, who range in age from 30 to 40. "We developed our own fantasy worlds and invented characters." Dad was a pianist who moonlighted as a salesman. Her mother, Margaret, 57, is a nurse, now living in Seattle, where she and Nora's father moved in 1974. "My parents were poor," says Dunn, reasoning that they simply had too many kids. "We didn't have toys, we had tires."

Nora attended Providence-St. Mel High School, but after racial problems broke out, she transferred to a boarding school, St. Mary's Academy in western Illinois. After graduating in 1970, she went to the Art Institute of Chicago for two years to study painting, then moved to L.A. "I went to the beach a lot and just tuned out," says Nora, who worked as a waitress to pay the rent. After moving to San Francisco in 1976, she took some acting classes at City College and saw an agent who asked what she had been doing for the last five years. "I went to see Dr. Zhivago, and I guess I just dozed off," she cracked. Dunn didn't find enough interesting dramatic roles for women, so, with her knack for one-liners, she turned to comedy in 1981 because she felt she could create her own parts doing stand-up work at local clubs.

In 1983 Dunn moved back to Chicago, where she lived with her brother Kevin, an actor, and played more comedy clubs. It was Kevin who auditioned for SNL first. He told SNL writers Tom Davis and Al Franken, "You think I'm funny, you should see my sister." They did. Nora was hired; Kevin wasn't. He says he was "initially disappointed," but harbors no resentment. Kevin chuckles, thinking of their "bohemian days," when they didn't have any money to pay bills. "We hung out together and liked to dream about the future," says Kevin, 31, who has since moved to L.A., where he played Shelley Hack's assistant last year on ABC's sitcom Jack and Mike. "But I guess we weren't dreaming, because some of those things have come to fruition." Nora recalls those days of poverty as "the most free of my life. We certainly lived great. I remember if I had $20, I'd buy a bottle of champagne before I'd send money to the phone company."

She doesn't fret much about bills anymore. But her six-day (and-night) work schedule leaves her exhausted. "I work about 500 hours a week," says Dunn, who lives in a sparsely furnished one-bedroom apartment in a brown-stone in Manhattan's Greenwich Village. "Ray worries that I push myself too hard." Hutcherson spends about two weeks a month in New York during the SNL season. He uses the rest of the time to concentrate on his writing in Chicago, where they live the remainder of the year in an apartment on the North Side. Kids are on hold until Dunn can figure how to devote as much time to them as she does to her husband and career. She hopes to stay with SNL for another year and then would like to try writing movies. But, she says, "I won't do anything unless there's some funniness to it." If Nora's in it, consider it Dunn.