Unpleasant people meet unpleasant ends at a remote motel that Tony “Psycho” Perkins would have loved in “Identity,” the slick new puzzle-thriller from the director of “Heavy.”

It was a dark and stormy night. We’re in the desert. Rain is washing out the roads.

There’s a car accident. A family, John C. McGinley, Leila Kenzle and Bret Loehr, is shattered.

A shrewish actress (Rebecca DeMornay in full “Sunset Boulevard” mode) and her do-gooder chauffeur (John Cusack) are involved.

The phones aren’t working. The only sanctuary is a seedy motel, where Larry, played by John Hawkes, presides.

Others show up: the hooker, played by Amanda Peet, the unhappy newlyweds (Clea DuVall and William Lee Scott) and the cop and his prison-transfer (Ray Liotta and Jake Busey).

To complete the set up, we’ve spent the opening credits listening to tapes of psychotherapy sessions between a doctor (Alfred Molina) and a mass murder suspect.

The folks in the motel start meeting untimely ends.

Everybody has a secret. Everybody is a suspect. Is the convict loose? Is he the mass murderer, out killing again? Is it his minder, the cop? Why does the chauffeur have a gun?

The desk clerk at the motel is creepy; the unstable husband of the accident victim (McGinley) has a few screws loose.

It’s a classic plot, handled in lean and mean form by James Mangold, who also made the underrated “Cop Land.” No cheap scare is missed, no chance to shock is passed up.

It’s a film where someone is bound to say “Remember that movie where …” But the plot is as old as Agatha Christie, or the guy her “Ten Little Indians” was inspired by, Edgar Allan Poe.

But then the twists kick in. There’s a late-night death penalty appeal going on in the state capital.

The victims and the could-be murderers have odd connections.

The dead give-away here isn’t the director, who likes plots that fold in on themselves like this.

It’s the presence of Cusack, who has become a sort of brand-name for the odd, the quirky and the interesting. His character, like the others, feels like a caricature. He has Jean-Paul Sartre’s “Being and Nothingness” open on the front seat of his limo. He’s the moral center of the movie.

As the bodies pile up, the parallel stories collide and give conflicting versions of reality. You question who is doing what to whom before Michael Cooney’s script suggests that you should, and long before he over-explains what just happened for you.

Like the recent and less-successful “Basic,” this is a movie that jams a lot of its surprises into an elaborate and overlong final act.

Still, it’s involving the way few slasher films of recent memory have been.