You’ve seen that face before. In fact, you’ve probably seen it multiplied times 100 in The Matrix. But Australian actor Hugo Weaving—unlike compatriots Kidman, Crowe and his Hedda Gabler costar Cate Blanchett—isn’t a household name stateside, despite his role as Neo’s ubiquitous nemesis in the 1999 sci-fi thriller and an equally high-profile turn as the pointy-eared elf king in the Lord of the Rings series.

But Weaving seems fine with that. “As an actor, it’s much easier to do your job if your own personal image isn’t larger than the character you’re portraying,” says the 45-year-old, who first registered on the American radar in 1991 as a blind photographer in Proof, then in 1994 as a drag queen in The Adventures of Priscilla, Queen of the Desert.

In Hedda Gabler, Weaving plays the charming, manipulative Judge Brack, confidante of Blanchett’s scheming Hedda. The two actors worked together in LOTR and on the Australian picture Little Fish (opening in New York Friday 24), and for Weaving, the reunion is a happy one. “The relationship between Brack and Hedda is very playful,” he says by phone from Sydney, where he makes his home. “There’s an enjoyment of each other’s wit. Of course, all the characters are also trying desperately to dominate one another. Every time you have a scene with three people onstage, two of them are forming a temporary alliance.”

Live theater has a powerful appeal for Weaving, who like Blanchett, trained at Sydney’s National Institute of Dramatic Art. “You feel as if real people are existing right before your eyes,” he says. However, the stage has its perils, too: During a 2000 performance of The White Devil, he blacked out as his character was being strangled to death—a literal showstopper. But even though pistols are waved, fired and even pointed at Brack during Hedda Gabler, Weaving is undaunted. “I trust Cate,” he says. “She won’t shoot me.”—Tom Beer