Rising from the couch in his Manhattan apartment overlooking the Hudson, the 6'5" giant shambles to a wall displaying the mementos of his 63 years. There's a Jazzman of the Year plaque, a Jazz Hall of Fame certification and four Grammy nominations, all marking a more than 60-LP career as a master of the tenor sax. "Yeah," Dexter Gordon says in a husky whisper that makes you bend forward to pay attention, "all that's left now is the Oscar." There's a challenge in his laugh. Paul Newman, check your pool cues. You just might get hustled again.

Gordon, who appears in the low-budget ($3.5 million) Round Midnight, shapes up as The Color of Money star's stiffest competition in the Oscar race. Newman used the Actors Studio and 45 movies to learn his craft. While for his first major acting role (he did a walk-on in the 1955 prison drama, Unchained), Gordon drew on his own ruinous life on the road, jamming and for much of the 1950s, junking on heroin. He drew a 20-minute standing ovation at the Venice Film Festival last month. As he says in the film, "My life is music, my love is music, and it's 24 hours a day." The film is awash with that music—recorded live—with jazz greats such as Herbie Hancock, Wayne Shorter and Bobby Hutcherson backing Dexter. But mostly Round Midnight shows the toll that music took on the man.

Dale Turner, the booze-battered jazzman Dexter plays onscreen, is a fictional character. But his story shares elements of Dexter's and those of his bebop jazz contemporaries, including saxophonist Lester Young and pianist Bud Powell (the film is dedicated to both). These men were experimental artists, often uncelebrated at home; a few of the luckier ones found work and appreciation in Europe. "There's a lot of jazz history in the film," says Gordon, puffing cigarettes and sipping tea prepared by his wife, Maxine. "I tried to make it real and honest about these men, how they'd been tricked and taken advantage of. They were artists who had to cadge drinks in bars, and when they died you had to put on a benefit to bury them."

Round Midnight's French director, Bertrand Tavernier, a jazz buff, had decided from the beginning to cast "a musician, not an actor playing a musician." After viewing hundreds of old film clips of jazz greats at work, he was struck most by Gordon. Says Tavernier, "It was the way he moved his hands," graceful poetic extensions that punctuate the air, playing some imaginary instrument as he speaks. With the help of Henri Renaud of the CBS jazz department, Tavernier tracked Dexter down in New York in June 1984. At Gordon's apartment, Tavernier recalls, "I had to wait because he was sleeping, but when he entered the room I was really affected." Though Gordon has been off drugs since 1960, the cumulative effect of 40 years on the jazz circuit had left him exhausted. "Watching him I had the impression he was going to fall down," says Tavernier. A sapped Gordon had stopped doing club dates three years before, depending on recordings and royalties for a living.

Doing the film didn't interest Gordon at first. "He thought I was crazy," says Tavernier. The director had more immediate concerns. "Dexter took two or three minutes to answer every question. He's an old 63. Every move takes him half an hour." But Tavernier knew that Gordon was a living embodiment of the jazz era. He had to take the risk. "I could not think of anyone else doing the part." For his part, Gordon wanted to present the jazz musician in a "dignified" light. "I was carrying the ball for all of them," he says. But it took more than determination to get the strength to work. "Everything was wrong," Dexter admits. "I've had 40 years of scuffling to get a gig, traveling hard on the road, playing in dives and breathing in what other people breathe out." He also developed a diabetes-related condition that caused his blood sugar level to fluctuate wildly and added to his fatigue.

To improve his health he and Maxine went to Mexico for eight weeks, where a holistic regimen of herbs, hibiscus teas ("I drank the bark off the trees," says Dexter), massages and rest helped restore some of his strength. But the four-month location shoot in Paris was a drain from the start. "Dex wanted to take a two-hour nap every day," says Tavernier, who also employed a doctor to keep watch on his star. Though drugs were never involved, Tavernier says there were times when Dexter imitated his character and got drunk. Dexter insists his drinking was "medicinal, that's all." The director is unstinting, though, in praise of his amateur actor's prowess. The lights, camera angles, retakes never threw him. "He was tremendous," says Tavernier, "much more aware than some actors I know." For Dexter, getting into character was absolutely no problem. "This is my life," he says simply.

Born in the middle-class section of Los Angeles now known as Watts, Dexter—a doctor's son—grew up dreaming about a life in music. His parents encouraged him. After playing sax sporadically for local bands, Dexter got lucky when a member of Lionel Hampton's touring band dropped out and Dexter was hired to fill the spot. "I was 17 and I just up and left," he says. "I mean this was it. I had always wanted to be in a sharp big-name colored band."

Dexter's maturation took place on the road. "I was just a young cat coming up, looking to my elders," says Dexter. "I could never learn in college what I learned there." Even prejudice—being confined to the black neighborhoods of town—never drained his enthusiasm. Through the early 1940s he was making up to $100 a week, playing with Louis Armstrong, Billy Eckstine and Fletcher Henderson. Later in the decade he headed to Harlem, where he started the bebop music era with Charlie Parker and others. "I don't think there was any place more exciting to be," says Dexter. "Nobody dreamed about going on the bandstand without a silk shirt and tie, and there were all the brown-skinned beauties. It was a dreamland."

At least until Gordon took to heroin. In the beginning Dexter thought the drug was just fun. "I loved shooting up," he says. "Part of the charm, the romance, is the ritual of sticking a needle in your arm. It's like chopping up cocaine on a mirror." He also did it because it became "cool" in the jazz milieu. "We were the revolutionaries," he says. "We did what was new and hip with no forethought of consequences. Heroin just became part of the scene."

He moved to L.A. in the early '50s, got married and had two daughters, Dee Dee, now 33, and Robin, 34. He hospitalized himself for heroin addiction several times but slid back every time. "You know it's dumb, right? But next thing you know, there you go again." By the end of the '50s, "I had to shoot up before I played, and it got in the way of my jobs. I didn't get fired but I didn't get hired either. People didn't know when or if I'd show up."

It took a three-month prison sentence in 1960 to get Dexter off heroin. Arrested in L.A. for being a user ("I was easy to spot. I had the marks"), Gordon's incarceration at the California Institution for Men in Chino convinced him that he had to quit. "Finally I said, 'Dexter, no more.' What worked was, I didn't like it anymore. You dig? I didn't want to be around people who were like I was."

After his release, the divorced Dexter had trouble finding jobs. Though he was completely cured in 1962 when he went back to the New York jazz circuit, the police wouldn't issue him the cabaret card that was required for performing in Manhattan. Thus when he was asked to play in Europe he saw a sanctuary. "I went for three months and stayed for 14 years," says Dexter, whose popularity steadily increased in Denmark and Scandinavia. "I came alive over there," he says.

His return to America was engineered by Maxine, 43, a jazz tour coordinator, who became his manager in 1976 and wed him six years later. ("I married the boss and retired," she jokes.) Maxine convinced Dexter that there was a need for him and his music in America. "I could see people missing me—but needing me?" says Dexter. His widely heralded return in 1976 resulted in sold-out club engagements in New York and on tours for the next seven years. But in 1983 Gordon made his last public performance in Morocco. "I just got exhausted," he says. "I didn't have any resources left."

What he did have was a nurturing family. For the past seven years Dexter has lived in Manhattan with Maxine and her 8-year-old son, Woody. Dexter and Woody watch nearly every sporting event on television; their favorites are football and baseball. Each year, usually in January, the family retreats to a rented house in the mountains outside Mexico City where Dexter goes for his health. "Most of his contemporaries are dead," says the watchful Maxine. "Dexter is one of the few jazz musicians who's been lucky enough to recover from the rigors of the jazz life."

Renewed acclaim has sparked Dexter's desire to perform again. "My sabbatical is about over," he says. "You haven't heard the last of me." Dexter will lead the musicians he performed with in Round Midnight in 10 European concerts next summer. He'd like to act again as well, and this time he's thinking of Shakespeare. "I'm the Melancholy Dane," he says, adding a smile. "I'd like to play Hamlet with a horn."