As Dave Brown, a sexist, racist, trigger-tempered police officer carving out his own definition of justice on the mean streets of 1999 Los Angeles, Woody Harrelson climbs to the top of the acting mountain. It's a monumental portrayal of a cop in meltdown – bruisingly brilliant and coiled to spring.

Director Oren Moverman (The Messenger), who co-wrote the script with James Ellroy, is a filmmaker with rare skills. He can let us inhale the toxic atmosphere of crime and corruption and then startle us with unexpected feeling. Dave has spent nearly 25 years on the force doing things his way, bending rules out of shape as a matter of course. His record is shadowed by the killing of a serial rapist that won him the nickname "Date Rape." But the department can no longer turn a blind eye when Dave is caught on camera beating a suspect. Comparisons to the Rodney King incident fill the air, something the department can't abide in light of a recent scandal involving more than 70 cops in the Rampart division charged with brutality, evidence tampering and cover-ups. Dave offers no apologies: "I am not a racist. Fact is, I hate all people equally." Assistant district attorney Joan Confrey (Sigourney Weaver, radiating fire and ice) wants Dave's head on a platter.

In the hands of a lesser director, that would be that. But Moverman cuts deeper. Without going soft, he refuses to let us ignore the humanity in Dave. And so we see this cop at home with his wife. Make that two wives. Anne Heche and Cynthia Nixon play the sisters Dave married and divorced in turn, having a daughter with each. Dave is fine sharing the same household, but the women are getting fed up. Dave is allergic to true connection. Yet we get the attraction – such is the force of the cop's appealing-appalling vibe. Harrelson dropped 25 pounds to make Dave a lean, mean sex machine. And it pays off in magnetism. At a bar, Dave picks up lawyer Linda Fentress (Robin Wright), and we see disaster coming. It does. But the erotic sparks are undeniable.

Moverman is merciless in laying out Dave's faults. The great cinematographer Bobby Bukowski uses the hard blaze of the L.A. sun to put Dave under a microscope that even investigator Kyle Timkins (Ice Cube) can't match. And as Dave tangles with a homeless informant (Harrelson's Messenger co-star Ben Foster) and his ex-cop guru (a terrific Ned Beatty), we understand that the trajectory of Dave's life is nowhere but down, down, down.

Yup, it could have been a bucket of bleak. But the electric talent of Harrelson and Moverman is too exciting to be anything but exhilarating. These two are playing a game of ferocity and feeling that makes others look like rank amateurs. No chance you'll forget Rampart. Only stupid Oscar voters do that. Thanks to Harrelson and Moverman, this baby stings.

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• Video: Peter Travers Reviews 'Rampart' and 'Chronicle' in This Week's 'At The Movies with Peter Travers'

“Ambling Alp”

The "Ambling Alp" was the nickname of the six-and-a-half-foot-tall Primo Carnera. Though the song is named after the Italian-born 1930s heavyweight champion, Yeasayer are actually paying tribute to boxing legend Joe Louis with this first-person psychedelic dance-rock tune. “I was always interested in writing a song that had boxing mythology in it,” Yeasayer’s Chris Keating said. “It’s pretty fascinating: There were so many amazing characters, and it was so closely entwined with 20th century history.” Yeaseyer also invokes German champ Max Schmeling and hints at the historical significance placed on the historic bouts between the Nazi-era boxer and the African-American Louis.