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If it were a book, who'd believe it? If it were a movie, who'd see it? Ah, but what if it were a music video? After all, everyone stays glued to MTV whether the characters seem to be made for each other or totally unlikely. So let's consider the principals. On the one hand, you have this absolutely gorgeous California cover-girl type—all teeth, hair, legs and MasterCard to boot. And then, on the other hand, you have this scruffy rock 'n' roller: dark, moody, looks like he was probably a hood when he was a kid. And these two are supposed to get married—on a boat in the middle of New York Harbor, no less—and live happily ever after? Come off it; it'll never fly.

But fly it did, when piano man Billy Joel, 35, married supermodel Christie Brinkley, 31, the Saturday before last. Real life being what it is, it wasn't entirely the storybook affair it might have been in a video. But it came close. For starters, the weather didn't exactly cooperate. It was a cold, drizzly day. But, hey, no big deal. "If it snows and sleets," said Brinkley beforehand, "we'll turn a nasty day into a great one." Then there was the matter of the guest list; of the 150 or so invited family and friends the celebrity quotient was alarmingly low. There was Paul Simon, Isabella Rossellini and a Stray Cat (not to be confused with a stray cat) named Brian Setzer, but that was about it.

Obviously the bride and groom didn't want a party peopled by paparazzi. Though Brinkley maintained they chose to have a nautical nuptial because of their mutual "love affair with the ocean," Joel was probably closer to the truth when he said, "The reason we're going on the boat is to get away from the press." On the day before the wedding, in their first-ever joint interview, both made clear that, as Joel put it, "the wedding is not something we want to go public about. We're not Charles and Di. We don't think of ourselves as royalty. We happen to be working people."

So they are, though of course they are working people for whom things have worked out quite nicely. They got married on World Yacht Enterprises' 147-foot boat, the Riveranda, which was festooned with a thousand white tulips; the Statue of Liberty loomed large in the background. The groom appeared a tad seasick, or perhaps he was just nervous. "How do I look?" Joel asked bystanders. "Is my cummerbund all right? Should I wear it higher or lower?" When a radiant Christie appeared on the arm of her dad, Don Brinkley, Joel turned fully around to admire his bride. "A huge grin really lit up his face," a guest said.

Christie walked down the paper runway carrying 50 long-stemmed ivory roses and wearing a Norma Kamali high-necked white satin gown overlaid with ivory lace and gold tulle. As she reached his side, Joel took her face in his hands and gave her a long, passionate premarital kiss. Then they exchanged vows, swearing to "honor and respect" each other's "goals and ambitions," all the while looking deeply into each other's eyes. "It was as if there was no one else in the room," reports a guest. When Judge Shirley Fingerhood completed the seven-minute ceremony and proclaimed them man and wife, they went into one of the most exuberant hugs ever witnessed, while James Brown's I Feel Good blared forth from the speakers. As the boat rounded the tip of Manhattan and headed for the site of the reception, the Water's Edge restaurant in Queens, Brinkley tried out her new term of endearment. "Where's my husband?" she asked no one in particular. And when he materialized: "Have you met my husband, Billy Joel?"

Fans and photographers strained vainly at barriers 100 yards away as the bride and groom disembarked for the party they were determined to keep private. At the reception Joel and Brinkley dined on swordfish at a table for two. They danced to a Strauss waltz and fed each other pieces of the five-tiered wedding cake. Billy's mom, Rosalind, told guests that her son was such a loner as a boy that she sent him out when he was 5 years old with the specific assignment of finding a friend. Billy did a pretty good job, considering the fact that the kid he brought home, Bill Zampino, served as his best man on this day 30 years later. Somewhere around 11 p.m., the deejay put Uptown Girl on the turntable, but the guests who turned to see Joel's reaction were disappointed. The newly-weds were gone.

It had been a private, joyous day of the kind their fame makes hard to find. In the days before the ceremony, the two at times had seemed dazed with happiness. Interviewed the day before the wedding, Joel said even his family was "totally thrilled. And not just because she's a celebrity or the money thing or anything like that," he added. "They think she's a real sweet person, which she is, who's made me very happy. A lot of people have told me that—that I'm so happy. I feel happy. I must have been a real drag at one time."

He was stung, however, by some suggestions in the music press that he was "selling out" his working-class origins. "I happen to think that the people who like my music are not mean spirited, and I don't think they would deny me some personal happiness," he said. "I'm not marrying this woman because she's a high-fashion model. She's a wonderful person. It bothers me that people could think I'm motivated by things like that. I've never sold out. I work as hard on my music as I always have."

Not for the next few days, though. "I feel like I've been working real hard, and I'm going to let go and enjoy myself," said Christie of their honeymoon. Joel's only clue to their destination was that it would be somewhere "sunny." Perhaps it's the kind of place where they can sign the register "Rocky and Sandy Shore," as they have in the past.

It was on the rocky and sandy Caribbean island of St. Barts that Joel and Brinkley met two years ago. That was shortly before her longtime boyfriend, race-car driver and heir to the Moët & Chandon champagne fortune Olivier Chandon, was killed when he plunged off a Florida track into a canal. Though they had stopped dating each other a few months before the crash, Brinkley was nonetheless devastated by Chandon's death, but she found solace in her new friendship with Joel. Brinkley encountered Billy doodling on a hotel piano. "He recognized her," reports a friend, "but she didn't know who he was." After Joel introduced himself, Brinkley joked that she "couldn't take anybody named Billy seriously" and proceeded to call him Joe, a nickname that, friends say, has stuck. "I had this image of her," recalls Joel, "as this high-fashion model. I thought she was going to be a snob and that if she's that beautiful and blond, she can't be that bright. She turned out to be extremely intelligent." Within a month their names were linked in gossip columns throughout the country.

Joel was going through a rough period himself at that time. He had just been through a difficult divorce from his wife and former manager, Elizabeth Weber, and he admits that he and Christie met on the rebound. "We've both been through a lot of personal tragedy," says Joel, "and we sort of met on that level, like people who have been through the mill. We weren't starting out like teenagers; we weren't even looking to fall in love. It was a zap when it happened. It was chemistry."

For Brinkley, Joel was a man with a gift, as well as someone who offered substance and security after her two years with the rich and reckless Chandon. "It's more than the fact that he's a name entertainer," Brinkley says now. "He was a strong support for me [after Chandon's death]. He's a wonderful person, and, you know, it's his heart and soul, his mind and everything that made me want to marry him."

Billy and Christie come from entirely different backgrounds. Christie was raised by her mother and father, a TV producer, in Pacific Palisades and Malibu. Billy was raised by his mother, an office worker whose husband left home before Billy turned 10, in the blue-collar suburbs of Long Island. Bitten by the Beatles bug at 14, Billy rocked his way out of a high school diploma (because of poor attendance, not poor grades) and recorded his first LP in 1968 with a group called the Hassles. A tough guy as well as a rocker, Joel also became a successful amateur fighter, boxing his way to a 22-4 record. Meanwhile, across the continent, Brinkley was, by her own reckoning, a chubby-cheeked ugly duckling dreaming of becoming an artist in Paris.

In 1972, the year Joel's first solo LP, Cold Spring Harbor, was released, Brinkley moved to Paris to fulfill her fantasy. By 1975, when Billy's Piano Man went gold, she was making a good living as a model and was married to French illustrator Jean Francois Allaux. By the time Christie divorced him five years later, she had twice made the cover of Sports illustrated's annual swimsuit issue, and Joel was selling out concerts in the U.S. and Europe.

When they met in 1983, Brinkley and Joel had two of their biggest money-making years ahead of them. Christie stands to make millions from her line of sportswear, now in its second successful season, and Billy's Innocent Man LP has sold nearly 4.5 million copies. "This isn't a marriage," cracked a financial analyst at the wedding. "It's a merger." If so, it is a merger with a heart. Inspired by Joel's participation in the USA for Africa recording session, Brinkley has thrown herself into launching the Warm Project to aid Ethiopia. Using her connections and influence, Christie has gotten commitments from designers and models to stage a fashion-show benefit next fall. Now she wants to expand by convincing retailers to set aside locations in their stores for a "Warm" boutique and workshop. Designers would donate one-size-fits-all fashions to the shops, whose proceeds would help those suffering in Africa. "I'm real proud of her," says Joel. "She's a real go-getter."

As they settle into married life, Joel and Brinkley will keep an apartment in New York and buy some waterfront property outside the city. Billy will continue to tour but not as much as he once did ("I'm not 21 anymore," he points out), and Christie will keep modeling—don't forget what they said about each other's "goals and ambitions." And kids? No immediate plans, but Billy says, "I'd like to have a big family." Adds Christie, "I love kids. I would never let a career interfere with having a family." Right now, they are clearly awash in mutual admiration. "She feels Billy's the big star," relates a close friend. "She thinks she's marrying a highfalutin guy, while he thinks he's marrying the most beautiful girl in the world. He thinks, 'Wow, Christie Brinkley!' And she thinks, 'I just married Billy Joel! Can you believe it?"

Good going, guys—and congratulations. Maybe there could be a video in this after all.