TELEVISION : Miss Almost Perfect : Courteney Cox is beautiful and funny, which helps because she stars in the hit comedy series ‘Friends.’ So we can forgive that she’s a neatness freak too.

She made the cover of Rolling Stone with her pals from TV. People magazine chose her for the cover of its “50 Most Beautiful People in the World” issue. Her show--on which no less an expert than “Cheers” maestro and quintessential sitcom director James Burrows said she acts as the hub--is one of the biggest hits on television, ranking No. 1 for the first time the week of June 5.

All this notoriety after virtually disappearing from the limelight more than five years earlier. What gives?

Maybe it’s the eyebrows--which, she told People, she has been known to pluck to perfection for up to two hours at a time.

“Let me set the record straight,” said Courteney Cox, 31, one of the six stars of NBC’s hot series about young singles, “Friends.” “The magazine quoted me saying that I only have to do three things to look halfway decent. But I didn’t say only . I said, ‘Three things I have to do’--that are an absolute must. I have to fill in my eyebrows, put on some lipstick and curl my eyelashes.”

Then, pausing to think for a moment about whether she could offer admirers any other tips, she deadpanned: “Well, actually, plucking my eyebrows is more of a hobby than a grooming tip.”

Pretty women aren’t supposed to be funny. It’s a stereotype that Cox has had to fight, said Marta Kauffman, one of the creators and executive producers of “Friends.”

That fight is in part necessary because throughout much of her career Cox has been cast for her looks. Her big break came when Brian De Palma chose her from an audition of hundreds to play the young woman Bruce Springsteen pulls out of the crowd in his 1984 “Dancing in the Dark” video; she didn’t get the job as a result of any dance training. Then, in 1987, she was cast as Michael J. Fox’s girlfriend for the last couple of seasons of “Family Ties,” playing the straight woman to Alex Keaton.

Even her most prominent movie role, as Jim Carrey’s love interest in “Ace Ventura: Pet Detective,” highlighted her ability via her mere presence to make the kooky man seem lovable, rather than her own comedic flair.

“Let’s face it, she’s adorable and intelligent and really together. She is Monica,” Kauffman said, referring to the motherly, responsible, compulsively tidy character Cox plays on “Friends.” “She has the neatest dressing room. She even cleans up the other actors’ dressing rooms because she won’t go in there if they are too messy. Yet at the same time, she can do things that are unexpected and wonderful and really funny. Courteney is sarcastic. She makes me laugh all the time. We’re really lucky to find an actress who can do that.”

Much of her comedy on the show is born of playing against her Miss Perfect image. Monica makes a fool of herself as a klutz in a tap-dance class--something seemingly unimaginable to any casual observer of the athletic-looking actress. The character flips out after she discovers that a randy sex partner is only 17. And she is so compulsively neat that just her facial expressions of discomfort at one of her friends’ messing things up in her apartment is enough to provoke genuine chuckles.

“It’s funny, because I never think of myself as Little Miss All-Together,” said Cox, emoting a rather persuasive display of surprise at the tag during an interview, for which she is curled up on a sofa in the lobby of a plush Santa Monica hotel. She is wearing a baggy blue denim shirt and lint-free black leggings.

“I just don’t. But I guess that’s the perception people have from ‘Family Ties,’ where I wasn’t the funny one. And ever since, I’ve had to break through that. Even now some casting directors think they know me before they see me. But that was more than five years ago.

“And that’s why I love Monica, because not only is she a grown-up, and that’s good for people to see, but I can bring more of my own personality to her, and I’ve never really been able to do that before. She can be goofy and angry and sarcastic and a little bit naughty. People think of her sort as the goody-good and the prude on the show, but I think she has more sex than any of the others.”

So Courteney Cox isn’t perfect?

“OK, I am a neat freak. Not about myself. I don’t use a lint brush or anything, and I don’t iron, but I could easily pick lint off of someone else. I was doing, I think it was ‘The Jon Stewart Show,’ and I was picking things off of him and I thought, ‘Oh my God, I’m just like Monica. This is too scary.’ I have a lot of glass in my house, and I remember saying as a joke once that I clean my stuff with Windex while my friends are over, but then I found myself actually doing that the other day. It’s horrible.”

Power yoga, a vigorous rather than meditative variation of the discipline, has calmed her down a bit, she said. If friends come over and move around a stack of magazines on her coffee table, for example, she’ll now wait until they leave before fixing it.

“Am I neurotic enough for you?” she asked, laughing. “I mean, it’s a wonderful compliment to be thought of as the perfect girl. The People cover was really nice, and it was nice to get recognized on my own and not as a part of the group from the show, though I love all the stuff we’ve done as a group.

“And then, as soon as it came out, I started thinking, ‘Oh, God, now I have to put makeup on and stuff when I go out.’ I can be a real slob, and now I’m worried that people will see me and say, ‘ That’s the beautiful girl? Gross.’ ”

Mostly, though, she has enjoyed her recent reintroduction to the limelight. Getting recognized on the road by guys in big trucks yelling, “Courteney Cox, ‘Friends,’ cool, marry me?” is still a kick, she said.

All those guys will probably be happy to know that tabloid reports of her engagement to Michael Keaton, with whom Cox has been romantically involved for a number of years, are untrue.

“I bet that three-carat diamond is really beautiful,” she said. “But I never saw it.” In fact, recent rumors suggest that the two have separated, but she demurs when asked about the current status of her relationship with Keaton.

‘I love that the show has taken off, but this big thing about when you’re hot and when you’re not, I really didn’t notice the difference. It happens gradually, and after ‘Family Ties’ I was working, even if no one heard about it. The safest route at that point would have been to do another television series right away, and I could have definitely been another girl in a sitcom. Easy. But I really thought I needed to try other things.”

She parlayed her high profile into parts in several films, although even hard-core videophiles would be hard-pressed to remember “Mr. Destiny,” “Blue Desert,” “Shaking the Tree” or “The Opposite Sex.”

The Alabama-raised ingenue said she basically fell into acting after moving for a summer to New York after high school, scoring commercials for Noxzema and Maybelline. The thought of becoming an actor just never seemed within the realm of the neighborhood’s imagination back in Birmingham, she said. But the big breaks came fast and early, and, Cox said, she really didn’t feel comfortable or accomplished in any way as an actress until she left “Family Ties” in 1989, worked and struggled.

Although “Ace Ventura” was a huge hit and transformed Carrey into one of Hollywood’s superstars, it failed to boost Cox’s career, she said, because all the attention went to him. What landed her “Friends,” she believes, was her work in a dead-on-arrival sitcom, “The Trouble With Larry,” that lasted only a couple of episodes in the fall of 1993.

“No one had ever seen me like that,” she said. “I was mean and I was the funny one, and from that I was recommended for ‘Friends.’ I decided I could go back to TV because I just felt I had to keep working. And it was time for people to get to know me again. You need to rekindle your Q [Hollywood shorthand for TvQ, which measures name recognition and popularity]. You need to get out there because it does fade out pretty fast.”

That’s unlikely now, although Cox is a bit glum about NBC’s plan to move “Friends” from its golden spot between “Seinfeld” and “ER” to 8 p.m. Thursdays come fall. She said she has no doubts that the show will remain popular, but its ratings are expected to dip with the earlier start.

Although the inevitable backlash against any top dog has begun in the form of other sitcoms throwing biting barbs at “Friends,” Cox is comfortable, even flattered, by the potshots. The show is fast and funny every week, she said, and the warm, fuzzy message--that friends will love you no matter how big a jerk you are--is something she can endorse for five years and beyond, should the show run that long.

She hopes, however, that she’ll also be able to squeeze in some kind of movie work during her summer breaks--perhaps even a role as the comic lead.

“Yeah, I can see that,” producer Kauffman said when asked if Cox could graduate to big-screen comedy a la Sandra Bullock or Meg Ryan. “She’s certainly funny and beautiful enough, and Courteney also has a great deal of heart. Sure, why not? She could be the center of a movie. But how often do they let the funny, pretty girl be the center of a movie?”

Well, surely more often than anyone looks at Courteney Cox and says, “Gross.”