Adapted from one of Robert Ludlum’s bestsellers, The Bourne Identity was one of the exciting entertainments of 2002. Matt Damon played the hero, a man hauled out of the drink who digs two bullets out of his back and finds a Swiss bank account number implanted in his hip. He has no recollection of who he is, but he’s exceptionally strong and resourceful. Eventually he discovers he’s Jason Bourne, the graduate of a covert CIA program for assassins called Treadstone, and that at some deep level his humanity recoiled from a mission and he couldn’t complete it.

Bourne then teams up with Marie (Franka Potente), a young German who agrees to drive him to Paris. When the head of Treadstone puts out hits on both them, suddenly she’s bound to him and, inevitably, they fall in love. At the end of the film, Treadstone is gone (along with its chief) and Bourne and Marie have escaped the CIA’s prying eyes.

The sequel, The Bourne Supremacy, again based on a Ludlum novel, is directed by Paul Greengrass, the maker of the docudrama Bloody Sunday. He brings such sophisticated technique to the opening scenes that they run through you like an electric current.

In short order, an operation that’s supposed to be monitored by one of the CIA’s new stars, Pamela Landy (Joan Allen, acting in her patented chilly, tight-lipped style), goes disastrously wrong, her undercover people are murdered, the killer frames the long-absent Bourne, and someone tracks him down in India, where he and Marie have been dodging the CIA. The editing of these episodes is so intricate as to seem almost subliminal, and the flashback images Jason has been struggling to grasp—with Marie’s patient assistance—are rendered as shards of color whose collision is visceral and prismatic. At the climax of the spectacular introduction, the car Bourne is driving is shot into the sea: he gets himself out, but by the time he reaches Marie, it’s too late.

Greengrass’s filmmaking is superior to the material (Tony Gilroy wrote the script), and the gap widens once he’s provided this beautiful kiss-off for Marie. Her character (and Potente the actress) supplied the core of feeling, and the romance, in The Bourne Identity. She also brings out the best in Matt Damon.Without Potente his performance is efficient but lacks an emotional hook. So does the movie, except insofar as Potente haunts it after she’s gone, just as the mermaid image of her death stays with us.

You keep waiting for the movie to be about more than its plot (Jason has to prove his innocence and find out who wants him dead), but Greengrass only transcends it on two occasions—both, perhaps not coincidentally, encounters between Bourne and a woman in distress. The first is Nicky (Julia Stiles), his Treadstone liaison, whom he terrifies in a desperate attempt to understand his first mission. The second is Irina (Oksana Akinshina), the daughter of an assassinated Russian minister and his wife, whom Bourne must free from her misapprehension that her parents died in a burst of domestic violence. Both actresses are superb.

Stiles had no character to play in the first movie; Greengrass remedies that error. And Brian Cox, shortchanged last time as the CIA bigwig who’s Treadstone’s secret benefactor, is in top form in a much-expanded version of his character. But Greengrass’s fine work with these actors only gives us a taste of what he might have accomplished with a more layered screenplay.

When Sam Peckinpah did his Ludlum movie, The Osterman Weekend, he broke the narrative apart and transformed it into a statement about our relationship to technology. Greengrass serves the movie he’s been handed, and he does it expertly. But the few resonant scenes make us impatient with the thinness of the rest.