The psychological thriller “The Little Things” feels like a throwback, in a not unpleasant way. It’s a big-studio movie that’s neither franchise film nor silly comedy, its top-heavy cast features three Academy Award winners (Denzel Washington, Rami Malek, Jared Leto), and writer/director John Lee Hancock sets the film in the time period it was written: the early 1990s, a time when cops used payphones and criminals didn’t carry convenient tracking devices. The film — which took Hancock 30 years to finally make — wallows in cliché, but intentionally so; the familiarity is part of this film’s taut appeal.

Washington plays Joe “Deke” Deacon, a sheriff’s deputy in rural California who, as we meet him, is reluctantly sent to Los Angeles on a quick assignment. He is, we quickly learn, that very familiar kind of movie lawman: a loner haunted by a past case, one that seems to be part of a series involving murdered young women. Deke soon forms an unlikely team with L.A. detective Jim Baxter (Malek) to track down a suspect, a creepy fellow named Albert Sparma (Leto) — but something unstated in Deke’s past casts a shadow on the investigation.

In other words, yada yada yada — you’ve seen cop movies like this before, and could probably recite that synopsis along with me. But “The Little Things,” despite an iffy title and a screenplay that could have used a little trimming, mostly works, should you be in the mood for an old-school detective thriller. And that’s due to the trio of interesting actors at its center, who play off each other with effortless skill. Washington — who could play this kind of role in his sleep, but mercifully doesn’t — now and then lets us see Deke’s gleeful grin; though he’s genuinely (and a bit too literally) haunted by the lost young women, he nonetheless loves the chase. Malek, whose unruffled, dapper character is Deke’s polar opposite, has an enjoyable way of always looking like he knows more than he’s saying. And Leto finds a breezy, theatrical menace in his very odd character: Is he a killer, or is he just malevolently strange? The three of them intersect in an enjoyably dramatic interrogation room scene; it’s like a sly three-way tango.

Ultimately, “The Little Things” doesn’t add up to much; its ending, particularly, is underwhelming. (You’d think in 30 years Hancock could have found something a little better?) But at a time when movie-star charisma is in short supply, it brings some somber but welcome diversion.

With Denzel Washington, Rami Malek, Jared Leto. Written and directed by John Lee Hancock. 127 minutes. Rated R for violent/disturbing images, language and full nudity. Streaming on HBO Max starting Jan. 29.