Sienna Miller says she didn't seek fame

NEW YORK - Her on-off relationship with

Jude Law made her an overnight celebrity, but

Sienna Miller says that wasn't her goal. "I was just never desperate to be famous, which I know sounds cliched and probably like a lie, but it is, in my case, very true," the 24-year-old actress says in the January issue of W magazine. "And that's the irony of my situation.

"It was always about acting, and now it's all about everything but that. I fell in love with someone very, very famous, and that's beyond all of our control. Strategically I probably could have analyzed it at the time and thought, `This could potentially be very damaging,' but that was a very beautiful period of my life."

Miller, a fashion icon and Hollywood It Girl, reportedly broke off her engagement to Law last year after he publicly apologized for cheating on her following reports that he had a fling with the nanny of his three children from his marriage to fashion designer-actress

Sadie Frost.

She says the 33-year-old actor remains "a very close person in my life."

"It just becomes this soap opera," she says, recalling the media attention. "And I guess I had a pretty good few episodes."

Miller stars as Andy Warhol muse Edie Sedgwick in the upcoming movie "Factory Girl."

"I know that I have a lot to prove to a certain degree, but it's fine," says Miller, whose screen credits include roles in "Layer Cake," "Alfie," which starred Law, and "Casanova," opposite

Heath Ledger.

Though she's been tagged as a party girl by the tabloids, Miller says socializing over alcohol was how she was raised.

"I was brought up in a culture where, when you're 12 years old, you're given a glass of wine at dinner — it was never a novelty," she says.

"Factory Girl," also starring

Guy Pearce as Warhol, is scheduled for limited release in the United States on Dec. 29.

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On the Net:

W magazine: http://www.style.com/w/