The first thing we see in "American Hustle" is Christian Bale putting together his hair. He plays someone completely bald on top but with long hair on the sides, and with the aid of some glue, a forlorn hair piece and a comb-over, he arranges himself in the mirror and goes out to face the world.

It’s an arresting and strange opening for director David O. Russell’s exuberant new film — arresting because there’s no taking your eyes off Bale, who looks awful, having gained 50 pounds for the role. (He gained the weight, not because he had to, but because that’s just the kind of thing he does.) And it’s strange because the spectacle leads an entire audience to temporarily disrespect the guy, when in fact he’s our hero. Even that hair is worthy of respect. Here is a resourceful individual who will do whatever he needs to do, including cultivating an illusion of hair in that distinctly hair-loving era of the late 1970s.

"American Hustle" is loosely based on the Abscam scandal, which was crazy enough even before Russell and co-screenwriter Eric Singer got hold of it. A sting operation by the FBI, in which various political office-holders were offered bribes on behalf of a (fake) Arab sheikh, it led to multiple convictions, as well as to charges that the FBI unfairly entrapped people.

The film changes names and motivations, adds characters and alters relationships, but one thing is true: The FBI really did hire a professional con man to put over the scam. Thus Irving (Bale), a man from the Bronx streets (Bale’s accent is perfection).

His partner is his girlfriend, Sydney (Amy Adams), who hides her own hardscrabble background behind a posh English accent. Both are driven by a need to reinvent themselves as something splendid and glamorous, which makes them quintessentially American dreamers, not just hustlers.

"American Hustle" is Russell’s best film, one that finds him in that ideal zone of spontaneity and complete control. He employs voice-over narration, then drops it when he doesn’t need it anymore. He dresses Bradley Cooper, as an ambitious FBI agent, in home-permed hair and garish ’70s fashions, and he gives him the freedom to act just as high-strung here as he did playing a manic-depressive in "Silver Linings Playbook."

Much is extreme, and yet in keeping with an era of vulgarity and bacchanalian excess.

As Cooper’s much-abused boss, Louis C.K. is the focus of some very funny scenes.

Yet the comedy doesn’t inhibit Russell ("Three Kings," "The Fighter") from dropping into an ominous mood when necessary, as when the FBI agent starts casting to land a mafia boss. Robert De Niro plays the boss as a no-nonsense old murderer, and he’s threatening enough, just sitting there talking, so as to hover over the rest of the movie like a poison cloud.

Jennifer Lawrence, as Irving’s young wife, embodies the movie’s tonal range. She is funny and alarming, often at the same time.

Rosalyn, who tricked Irving into a marriage he can’t escape, is a complete idiot who thinks she’s brilliant, and a monster of selfishness who thinks she’s giving. Lawrence’s performance lets us see the twists and turns of her thought processes, even as she masters an Eastern dialect and an outsize floozy manner that’s the antithesis of her usual screen self.

But it’s Adams and Bale who are the film’s heart and soul, the honorable crooks in a sea of piranhas, the movie’s truthful core around which all the madness revolves. Adams, who goes through the movie almost flopping out of her low-cut ’70s gowns and blouses, is especially poignant playing an intelligent person with the least power and the most at stake. It’s fascinating watching her think her way through as she does the most with a bad hand.

And Bale brings great suppressed feeling to his scenes with a good-hearted New Jersey mayor (Jeremy Renner), whose life Irving is being forced to wreck.

The re-creation of the 1970s will please everyone who was there and instruct everyone who wasn’t. Yes, it was crass. Yet the ’70s were like the 1920s, in that years later you can take one look and know the decade, and it wasn’t all ugly.