IN ONE SCENE in The Walker, Carter Page III (Woody Harrelson) tries to explain the ins and outs of a murder case: "It's not that simple." On the contrary, it's as simple as pie! Page is an alienated detective, and the wealthy lady (Kristin Scott Thomas) whom he's protecting from the cops is amoral and might be guilty. What could be less complex than that? Director/writer Paul Schrader (never to be forgotten for his script for Taxi Driver) is an ex–film critic and a man who remembers how efficient, atmospheric detective stories are crafted. Thus he leads this satisfactory mystery through a paranoid city: the end stages of the Bush regime in Washington, D.C. The capital and Salt Lake City are the two places, says a line of dialogue, where homosexuality still has to be kept under wraps.Page comes from third-generation tobacco money; his father was a senator who sounds very much like Sam Irvin. Page himself is a superficial idler. He spends one demure day a week at an upscale real-estate office. His real vocation is gossip, which he trades at a weekly canasta game with some aging Washington wives. His special friend among the quartet is Lynn (Kristin Scott Thomas), who is married to the minority leader of the Senate. One afternoon, he escorts Lynn to meet her lover. The man has been stabbed to death. Page doesn't care much for the corpse, who once scalded him in a bad business deal. As he tells the police, "I didn't say we were close. I said I knew him for 20 years." Page wants to keep his life discreetly compartmentalized. In the dark hollows of a gay bar, he meets his Palestinian boyfriend (Moritz Bleibtreu), who is creating an explicit series of photographs based on Abu Ghraib as protest art. Since Page is the prime suspect in the murder, thanks to a homophobic U.S. attorney (William Hope), he is especially eager to avoid any exposure of his personal life—even as someone sends a hit man after him.On his low budget, Schrader creates an atmosphere of big money. It is the Bresson fancier in him that makes the environment speak louder than the characters. The movie looks rich: a framed embroidered antique kimono on Page's bedroom wall. Bryan Ferry's voice echoes down the hallways. Pensively, Page prowls through his vast wardrobe and puts away his toupee (no doubt the wig is Page's most secret shame), which has its own special nook in a dark wooden cabinet. Washington movies usually stress the drab, transitory nature of the town; the flow of more permanent power is lushly visible here.

Page receives covert aid from the eldest member of his canasta circle, played by Lauren Bacall. She certainly understands this kind of movie, knowing its merits, playing it with great and sarcastic pleasure. She trades some clever trifling conversation with Page concerning the identity of the movie actor who has played the most presidents onscreen. (Hint: He just played Louis XV.) Harrelson's molassesy drawl and polished surface make this a most ingenious performance. One is willing to stick with him, drifting through the carelessly written plot and ignoring the occasional clinking line. It's probably time to stop telling the audience that the solution to a mystery is "Follow the money."

THE WALKER (R; 108 min.), directed and written by Paul Schrader, photographed by Chris Seager and starring Woody Harrelson and Kristin Scott Thomas, opens Dec. 14 at Camera 12 in San Jose.

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