Equally adept at playing a jewel thief (‘Snatch’) or a Mexican cop (‘Traffic’), he’s the moving target you can’t take your eyes off, the actor on every director’s most-wanted list.

It was Benicio Del Toro’s first day of work on the film Traffic, and already he knew things weren’t going to be easy. Never mind that the movie, a triad of intersecting drug-trade stories, required him to play most of his role in Spanish, or that it needed an understated, quiet style of acting, light years removed from the bravura eccentricities with which Del Toro had made his reputation. The real problem was that the day consisted of shooting two crucial scenes from completely different parts of the film—the first a standoff in a swimming pool, the second a tense hotel room conversation. In his slightly odd, charmingly oblique way, Del Toro decides that while it wouldn’t be true to call either of the scenes the heart of the movie, they were unquestionably “important organs”: The first, he says, might be the liver; the second the lungs.

Anyway, he had no sooner made the hundred-yard walk to his trailer after completing the swimming pool scene than an assistant director announced that director Steven Soderbergh was ready to shoot the hotel encounter. Del Toro, whose serious, thoughtful approach to every role is sometimes belied by the goofiness of his choices, was stunned. “I said, ‘Let me tell you something, bro: I am still wet,’ ” he recalls. “If you look at that hotel scene, my hair’s wet. It’s kind of weird, but it’s okay.”

You could say that last sentence is an apt description of the 34-year-old actor: kind of weird, but definitely okay. “I just think he’s cool,” says British director Guy Ritchie, who cast Del Toro as the stylish but ill-fated diamond thief Franky Four Fingers in his wild new movie, Snatch. “I think he’s got a good look, and I like the way you can hardly understand a word he says in his films. I don’t know, he’s just got something going on.”

Soderbergh was similarly fascinated by Del Toro after seeing him in The Usual Suspects and Basquiat (for which the actor won two consecutive Independent Spirit Awards), as well as the less-well-received Fear and Loathing in Las Vegas. “He’s one of those people that everybody in the industry knows well and respects and likes,” Soderbergh says. “I think he has movie star potential. I’ve always thought, ‘This guy’s gonna bust out at some point.’ And this [Traffic] seemed like a good place to start.” Already, there’s Oscar buzz about Del Toro’s performance, as a conflicted Mexican cop who’s waging a losing war on drugs. “That was the riskiest section of the movie, in that it was in Spanish and set in Mexico,” Soderbergh adds, “and it needed somebody really strong to keep the American audience paying attention.”

Once, the easy joke would have been that audiences need to pay attention to have any chance of understanding what Del Toro is saying (in light of his infamously mumbling turn in The Usual Suspects). But Traffic’s subtitles make his enunciation irrelevant—and besides, the guy really only switches on the mumble when he thinks the role demands it. In conversation, Del Toro speaks quietly but clearly, in a soft Puerto Rican accent; he’s completely intelligible, and he seems to be making sense until you play back his conversation on tape and realize that he’s still a little off: smart, serious, but also sincerely (and purposefully?) disjointed. This afternoon, he’s sitting in a nondescript restaurant a few blocks from his west Los Angeles apartment. A baseball cap from the LAPD SWAT team is pulled down low; beneath it, his hair is tangled and dark. “This is, like, my black period,” he says. “I’ve done four movies almost back-to-back, and my hair is black in every movie.” (Besides Snatch and Traffic, the other two movies are Sean Penn’s The Pledge and last fall’s The Way of the Gun.) He grins. “I can’t wait for my white period.”

Of course, Del Toro’s immersion in a role goes far beyond hair color. “He works harder than any other actor I know,” says Ryan Phillippe, a friend of Del Toro’s since they starred together in The Way of the Gun. “He works, from what I could figure, 90 percent of the time. After work, at home, he’s up all night working on his part. I’ve been known to do that on occasion, but it’s clear to me that Benicio does it every night. He’s incredibly committed.”

Still, it’s not always the fruits of his extensive research that come out onscreen. “When I saw myself in Traffic,” Del Toro says quietly, “I saw my dad. And when my brother saw the film, he said, ‘There’s a couple of moments in there that are just like dad.’ I wasn’t thinking about him at all when I was making the movie, but I think that the first person you start imitating, if you’re a boy, is your dad. That’s your first influence and maybe the most severe. And my dad was very much an authority figure. He’d been in the army, and he was strict. We had that thing . . .” He whacks his fists together to illustrate how he and his father were at odds. “Later, you recognize the value in a lot of those things. But at the time, I just thought, ‘No, I ain’t gonna do that today.’ ”