Though claiming no kinship with Abel Ferrara's original Bad Lieutenant (which Herzog insists he has never seen), the director delves happily into similarly murky moral territory. Set in a blasted post-Katrina landscape of abandoned buildings and echoing neighborhoods, the story centers on Terence McDonagh (Cage), a homicide detective crippled by back pain after rescuing a prisoner from rising floodwaters. (Herzog's protagonists are more likely than most to be punished for random acts of heroism.) When the Vicodin prescription no longer helps, Terry graduates to cocaine and heroin filched from the police evidence room. When that, too, is no longer an option, Terry is forced to become more creative.

By turns feverish and becalmed, familiar and surreal, Port of Call is a portrait of functional addiction dressed up in the finery of a traditional crime drama. Ostensibly investigating the murder of a family of illegal Senegalese immigrants, Terry seizes every opportunity to feed his habit and vent his eccentricities. Completely on board with these goals, Herzog fills the screen with hallucinatory images that may or may not be projections of Terry's mental deterioration: a dead gator in the middle of the highway, iguanas languishing on a coffee table. Not for nothing are the lizards singing "Release Me."

Pushing the character to a place almost beyond redemption, Herzog nonetheless never allows him to become repellent. As Terry dodges his bookie and the mob, shakes down young clubgoers for drugs and sex, or juggles a junkie-hooker girlfriend (Eva Mendes) and alcoholic parents (Tom Bower and Jennifer Coolidge), the film refuses to take him seriously. Peppered with humor every bit as weird as its protagonist, Port of Call encourages us to root for him; whether waving a gun at a pair of old ladies or partnering up with a volatile drug lord, Cage gives Terry an underlying sweetness that counters his behavior and derails our dislike.

Playing out in backrooms and beneath cement-slab skies, Port of Call evokes New Orleans mainly in atmosphere and with recurring images of water, some with offbeat religious undertones. Herzog may have been attracted to the idea of a floundering city, but he films it without landmarks, following William Finkelstein's serpentine plot through mostly anonymous locations: a rural shack, a dank jail, an assortment of seedy bars. Swerving from the earnest to the inane — sometimes in the same scene — the director parodies the genre while getting off on it, finding in Cage a broken muse of hard-boiled degeneration. Lurching around the battered city like a sad-sack nomad, stooped with pain and exhaustion, Terry is both hero and villain, vulnerable and invincible.

"A man without a gun, that's not a man," he says when his actions at last catch up with him. You get the feeling that Herzog, that dedicated chronicler of alpha-male lunacy, agrees.