NEW YORK – Dr. Juliet Burke reveals herself to be a complex character on “Lost.”

Or, rather, she reveals very little of herself. She is a combination of strength, cunning and wistful victimhood, all displayed on a face so enigmatic she could give the Mona Lisa a run for her money.

Introduced as one of the Others at the start of last season, Juliet has remained an object of delicious mystery, despite selective details parceled out by the show. Viewers still aren’t sure where her loyalties lie – or even if they should dare to like her.

The only certainty: Elizabeth Mitchell does a bang-up job with the role, keeping viewers teased at arm’s length even while drawing them in.

“I’ve had a tremendous amount of freedom to create something strange,” Mitchell says happily.

Questions will probably multiply with Thursday’s episode (9 p.m. EST on ABC) which is expected to give Juliet the spotlight.

Mitchell’s rule of thumb in playing her: Don’t act angry.

“She needed to be someone who could be a tremendous leader, who had an innate sense of power, but didn’t behave in an angry or strident way,” Mitchell says. “She needed to have a sense of toughness, but in a way the audience couldn’t quite grasp.”

Another thing about Juliet: her cool melancholy, which offers no hint of Mitchell’s effervescence and frequent smile.

The 37-year-old Mitchell grew up in Dallas, where, from childhood, she studied acting and performed in local theater.

“I wasn’t particularly good when I started,” she says. “I just felt a genuine love and excitement about the whole process. I felt safe onstage. And I had a really good memory.”

Theater helped her weather an ugly-duckling adolescence.

“I was horribly awkward, tall and scrawny, with frizzy, crazy hair and terrible acne,” recalls Mitchell, who is now an indisputable looker. “But it didn’t matter even remotely on stage: There, no one’s looking at your skin. I just spent a little extra time making sure everything was covered up. My way of thinking was, if I’m going to play all the characters I ever dreamed of playing, I need to be able to be both very unattractive and awkward, AND swanlike.

“I’m still working on swanlike,” she cracks. “I walk like a football player.”

Mitchell began her TV career in 1994 on the daytime soap “Loving,” and won acclaim four years later opposite Angelina Jolie in the HBO film “Gia.” She had the title role in the 2000 TV film “The Linda McCartney Story,” and played Mrs. Claus in the two “Santa Clause” sequels. Other films included “Frequency” and “Nurse Betty.” She had a continuing role on “ER” during the 2000-01 season. And she has starred in a remarkable number of promising but short-lived series such as “Significant Others,” “The Beast” and the Rob Lowe legal drama “The Lyon’s Den.”

“I always chose a role for the character and not for the show,” Mitchell says. “I never once chose a show because it was the ‘right’ career move – including ‘Lost.'”

Not that she wasn’t a fan of the show. She had been a devotee its first season.

The next year, she steered clear of it.

“I was pregnant and I didn’t watch anything that had any violence,” she explains. So when she arrived in Hawaii to begin shooting the third season, “I watched the whole second season in my trailer my first week. I really liked it. But I was shocked when those women (Ana Lucia and Libby, both gunned down without warning) got killed. That’s probably where my fear of dying on the show began.

“But I found the work to be so exhilarating, I decided: Until they fire me, I’m gonna just make this all that I want it to be.”

So far, so good. And aside from the unforgiving casualty rate among “Lost” regulars, Mitchell says she loves each script’s surprises.

“As an actor I never work with a complete idea of what the end is gonna be. I prefer to work with an understanding of what my character’s intentions are, what she’s trying to do – which is how we all go through life.

“I really identify with Juliet,” says Mitchell before hastening to draw the obvious contrasts. “I have quite a lovely life with my family (son C.J., now 2« years old, and her husband, actor-comedian Chris Soldevilla). Juliet doesn’t have that. She sits on this reservoir of anger and loneliness. That’s what makes me not know what she’s capable of. And I think that’s fascinating, that’s really neat.

“I think she’s scary,” says Mitchell, her smile luminous. “But I like it.”