Bad Lieutenant, Werner Herzog, 122 mins (18)

As someone asks the hero of Bad Lieutenant: "What are you acting so crazy for?" Ask a silly question: because he's played by Nicolas Cage, with whom you expect nothing less than full-on derangement.

Now, imagine the combination of Cage and director Werner Herzog, working together on a cop thriller, and you have the ultimate recipe for on-screen craziness. What about throwing in a few iguanas? And if I were to invoke the name of wild man indie director Abel Ferrara, that would give you some hint of quite how enthusiastically, irreducibly, joyously out there Herzog's Bad Lieutenant really is.

This exercise in streetwise pulp – to give it its full title, Bad Lieutenant: Port of Call New Orleans – is neither a remake of nor a sequel to Bad Lieutenant, Ferrara's 1992 exercise in drugs, sleaze and Catholic angst, with Harvey Keitel as a New York cop on the skids. Herzog disclaims all knowledge of, or interest in, the original – which hasn't exactly won him Ferrara's undying respect – but the two films share a producer, Edward Pressman. And there are a couple of key elements in common: such as Keitel's character, Cage's has betting problems and a tendency to harass hapless citizens. Otherwise, that's about all the two films have in common. They're not even about the same lieutenant.

While Ferrara's was very much art-pulp, exploring a spiritually-tormented dark night of the soul, Herzog has made a straight gritty thriller with the occasional surreal flourish. It was anyone's guess how the erstwhile master of German art-cinema poetics would fare on his first venture into American cop material. At a guess, his interest in the thriller genre was in the same spirit of exploration that previously made him visit Antarctica or an active volcano: it was there, and he'd never been there before.

Written by William Finkelstein, the film is set in New Orleans after Hurricane Katrina. After rescuing a drowning prisoner Cage's policeman, Terence McDonough, earns a promotion to lieutenant and a chronic back pain – which he thereafter tries to dull with any drug he can get, usually from confiscated evidence. McDonough is out to catch some killers, but we're less interested in McDonough investigating the hit than in Cage exploring the goofier byways of his acting style. As ever, Cage is strange even when not doing a great deal, from the monk-like haircut on: wearing an outsize suit and waggling his head like a wired marionette, he resembles an Egon Schiele sketch of The Joker.

This is the most unrestrained Cage turn since he gobbled cockroaches in the 1998 film Vampire's Kiss, but McDonough's high-narcotics diet makes the performance weirdly plausible. Cage manages to make his careworn cop feel real, and McDonough probably needs his suit's XXL shoulders to bear the weight of all his mundane problems: runaway witnesses, alcoholic dad, a dog to look after, not to mention the clients of his hooker girlfriend (a routinely sultry Eva Mendes), one of whom ("Ohhh yeahhhh!") momentarily outdoes Cage in the nutty acting stakes.

The film is a dazzling catalogue of seemingly impromptu flourishes: McDonough breaking out in giggles every time he mentions a mobster called "G", or his free-form crack-induced rant to some baffled gangsters ("To the break of dawwwn, baby!"). Cage also has a dazzlingly unpleasant but extremely funny scene in which he terrorises an elderly lady and her carer – a stroke of jaw-droppingly gratuitous outrage that makes the shocks of Kick Ass look like the kids' stuff they are.

Herzog too contributes his own spurts of wildness. There are relatively few of them, as he's taking his job as a genre journeyman seriously, and to good effect. But sometimes he can't resist throwing a curveball. There's the alligator that shambles distractingly across the scene of a traffic incident, and the iguanas which suddenly just appear – in delirious close-up, at great length and to the tune of "Please Release Me". And there's more: listen out for a burst of frenzied blues harp and the line "His soul's still dancing", and stand by for your jaw to drop.

And yet somehow, Herzog has made one of the most entertaining, no-frills thrillers to come out of the US in some time. You'd have to be an iguana, or Abel Ferrara, to dislike it.

Next Week:

John Walsh sees 4321, the latest from Noel Clarke, writer of Kidulthood, and writer, director and star of Adulthood