Back in 2003, Johnny Depp famously panicked Disney executives with his whacked-out turn as Pirates of the Caribbean‘s Captain Jack Sparrow — only to have the character become an instant icon. For the upcoming 3-D Alice in Wonderland, opening March 5, Depp decided to dive even further down the rabbit hole with an orange-haired, green-eyed, nonsense-spouting take on Lewis Carroll's Mad Hatter. Alice is Depp's seventh collaboration with director Tim Burton, and anyone who's seen the other films they've made together — including Edward Scissorhands, Ed Wood, and Charlie and the Chocolate Factory — knows they share a taste for, as Depp puts it, "the slightly left of center." Still, with this gonzo turn as the Hatter, Depp braced himself for a full-blown freakout in Disney's executive suites. "When we first went in to do the camera tests, I was thinking, ‘They're going to lose their minds,'" Depp recalls. "But Tim fully supported it. It was a couple of solid hours in the makeup chair everyday but it really helped. You start to understand who the guy is through all that weird kind of Carrot Top kabuki."

Alice marks Depp's first foray into the brave new world of 3-D filmmaking, but the actor (who admits he still hasn't seen Avatar) says he won't be able to fully appreciate that extra dimension. "I'm actually unable to see 3-D," he says. "I've got a weird thing where I don't see properly out of my left eye, so I truly can't see 3-D." Then again, he never likes watching himself onscreen anyway. "So I have an excuse this time," he says, laughing.

For more on Alice in Wonderland, plus an exclusive interview with Johnny Depp and Tim Burton about their 20-year partnership, pick up the new issue of Entertainment Weekly, on stands February 26th.