With a little help from Health Ledger. Within weeks of her bust-up with Burns (who is now engaged to model Christy Turlington), Graham, 31, was making sweet music with the 22-year-old Aussie actor, who was in Prague to film A Knight's Tale. That relationship ended in June, prompting Graham—whose other actor exes include Kyle MacLachlan and James Woods—to declare a hiatus from dating to concentrate on nonromantic pursuits. "I like cooking and having dinner parties, playing cards and doing yoga," she says. With two movies out this fall—From Hell, in which she plays a London prostitute, and Sidewalks of New York (due Nov. 21), which she filmed with Burns before their breakup—she has the career thing under control too. So what's up with the revolving-door relationships? "Heather is a rather freewheeling person with a lot of personality," says James Toback, who directed her in 1998's Two Girls and a Guy. "It's tough for her to find someone to fit her mold. She is not a simple person."
In fact, says Hughes, "she can be the hardest person to really know. Sometimes she can be really funny and smart and other times she can be very shy. She can throw curveballs at you." At Graham's 1997 audition for the sexually charged Two Girls, director Toback and costar Robert Downey Jr. tested her comfort level by discussing "strong, funny [read: raunchy] stuff," Toback recalls. While other actresses blanched, Graham "reacted by one-upping us for the next half hour. She was not one of the guys but a leader of the guys."
The elder daughter of James, 61, a former FBI agent, and Joan, 57, a children's book author, Graham was born in Milwaukee but grew up in Agoura Hills, Calif., along with sister Aimee, 30, an actress with whom she remains close. As a teen, "I had a long awkward stage," says Graham. "I had bad hair, bad clothes. I thought of myself as this nerdy girl." By the time she made her film debut at 18 in the teen comedy License to Drive, that stage had clearly passed. Says costar Corey Feldman: "I still remember thinking she had the best legs I'd ever seen." Other acting roles followed, including a part in the ABC cult series Twin Peaks, but Graham's breakthrough didn't come until 1997, when she played Rollergirl in the acclaimed Boogie Nights. Two years later she sealed her sexy starlet reputation as Felicity Shagwell in Austin Powers: the Spy Who Shagged Me. Her parents—strict Catholics—were apparently unimpressed: Graham has been estranged from them since 1996. "They don't like her doing these sexual parts," says Chen Kaige, who directed her in the upcoming drama Killing Me Softly. "She feels bad about the relationship." Graham told Talk magazine last February that she sought "a nurturing, loving environment," but "I just felt that I couldn't have that with them."
As for finding it with someone else: Content as she is with yoga and cooking, Graham, who splits her time between a Spanish-style L.A. home and a Manhattan loft, still has one eye open. "She wants to get married, have a family," says Kaige. "The question is, Who is the one she can spend the rest of her life with?" For now actors need not apply. "I think I'd like to go out with a writer next," Graham said last month. "I'm looking for someone with a laptop."
Lorenzo Benet, Julie Jordan and N.F. Mendoza in Los Angeles