Adrien Brody spends much of “The Jacket” locked in a large drawer, and, for most of this cryptic movie, we’re as in the dark as he is.

The title refers to the straitjacket Brody wears when he’s in that drawer, which is located at “an institution for the criminally insane,” a phrase you don’t hear much unless you’re in the 1950s. It works here, though — a near-future snake pit where patients walk around barefoot and where there’s a demented nurse who will make you think, “Wow, she looks just like Mackenzie Phillips would look if all the blood were drained out of her,” until the end credits, when you’ll discover it IS Phillips and, since she’s moving, she apparently still has her blood.

Adrien Brody, center, stars in The

Brody has been locked up for a crime he thinks he didn’t commit, and, while he’s in the drawer, he dreams he can travel through time. Or maybe he really does travel through time. Either way, in the future, he has the good fortune to meet Keira Knightley and the bad fortune to discover he’s going to die in four days.

Can he change the future? Can he prevent a crime from happening? Can he at least give Knightley some tips on how to improve her American accent?

These are the questions that occupy “The Jacket,” which isn’t quite as confusing as it sounds, particularly if you’re willing to disregard extraneous stuff that has no business being in the movie, such as the jarring prologue set in the Gulf War and the entire performance given by Jennifer Jason Leigh as a doctor in the institution for the criminally insane.

The movie doesn’t need Leigh’s character, but you can see why director John Maybury hung onto her. She’s entertaining, and she (along with Brody, who conveys warmth and hurt) gives the movie a soul.

The Jacket1/2 Find showtimes, trailers and more on the movie

Maybury is fond of carving up a conversation into a series of close-ups of eyes and mouths, a technique that ratchets up the intensity but tends to make the movie seem less like people talking and more like an installation at a modern art museum you never want to visit again.

Which is weird, because I do want to go to “The Jacket” again. Despite its ersatz artiness and loose ends, or maybe because of them, “The Jacket” raises unsettling questions about identity and about how accurately we perceive the world we think we live in.