Leonard can remember he hates being called Lenny. He can remember the job he used to hold and the wife he used to love. Just about everything else he knows, he learned from Polaroids, hastily scribbled notes and the crude tattoos all over his body.

Leonard, played with blank-faced concentration by Guy Pearce, is the frightened-yet-resourceful protagonist of Memento, a mind-pretzel of a thriller from writer-director Christopher Nolan. It made a splash at Sundance but couldn’t find a distributor—the main sticking point being that Miramax and the like doubted this insular, character-driven noir could find a nationwide audience. And oh yes—it’s told backwards, in increments of 15 minutes or so. A tough sell? Harvey Weinstein should have known better.

You see, Leonard has no short-term memory. He remembers his life before the night his wife was raped and murdered in their San Francisco apartment by somebody who also left him for dead. The culprit took his wife and his memory—and Leonard has pursued his revenge across the West, even though he usually can’t remember where he’s going or what he’s doing. He can’t hold a memory or a train of thought for more than 15 minutes. He relies on his pictures, his notes and his tattoos to confirm his identity and to keep his investigation on course.

There’s danger and intrigue in every parcel of this engrossing story, which retraces Leonard’s steps up the path of what could be the final hours of his quest to figure out who killed his wife. There’s also plenty of bleak humor: At one point, Lenny awakes from one of his slate-wiping moments and finds himself with an angry man after him. “So what am I doing? Chasing this guy?” Lenny asks himself. A bullet nearly takes his head off. “No, he’s chasing me.” Lenny runs.

Later—meaning earlier; catching on yet?—he runs into a few unsavory characters, among them a shadowy guy who might be named Teddy (Joe Pantoliano)—it’s only one of his monikers—and Natalie (Carrie-Anne Moss), a bartender whose motives don’t become clear until Leonard first meets her—that is, the last time we see her. It’s very much a writer’s movie, with little room for showy acting, and the cast cooperates with stark, Cornell Woolrich-meets-Elmore Leonard caricatures in their performances.

Due to its structure, the film’s climax is revealed in the opening three minutes. Instead of a whodunit, Memento becomes a whydunit. As Lenny moves toward what he thinks will be the resolution of the quest, we watch clues and solutions present themselves, then fade into the background when a new bit of information is gleaned from Nolan’s expertly folded script. Somehow, Nolan wrings tension out of the search for the beginning, not the twists and turns that lead to an end.

The strategy of telling a story backwards has been used by everyone from Atom Egoyan to Martin Amis, but rarely has it been employed within a story that made use of its suspense possibilities so well. Watching Memento for the first time is a profoundly disorienting experience, which creates an atmosphere of genuine tension.

We begin to place mental bookmarks throughout the tale, only to remove them minutes later. After a while, we understand the desperation enveloping Leonard, the desperation that led up to the first scenes of the film. There’s a hollow ring to the picture; as Natalie points out, even if Leonard gets revenge, he’s not going to remember it.

There’s no clear resolution in the final scenes of the film. As Nolan spent the first 100 minutes reminding us, even the best memories are faulty, and people often remember what suits them. That’s why the film’s final revelations are such a kick—we have no idea if any of this is true, or whether the events described are any more real than the lies we’ve already been told.

Those seeking concrete resolution to their stories might feel slighted, but they might also see the entertainment value in the mental exercise Nolan has presented for us. In many ways, it’s nothing more than an unsolvable Rubik’s cube, a puzzle that’s more interesting without answers. The more we learn about Leonard, the more information we’re forced to throw away. Both constructive and destructive, it’s a terribly entertaining exercise.

Memento (R) HHH1/2 Directed by Christopher Nolan. Starring Guy Pearce, Carrie-Anne Moss and Joe Pantoliano.