Tina Fey as Ariadne Oliver and Kenneth Branagh as Hercule...

 Tina Fey as Ariadne Oliver and Kenneth Branagh as Hercule Poirot in "A Haunting in Venice." Credit: Rob Youngson/Rob Youngson

PLOT Detective Hercule Poirot investigates a murder at an Italian palazzo.

CAST Kenneth Branagh, Tina Fey, Michelle Yeoh

RATED PG-13 (several shocks and scares)

LENGTH 1:43

WHERE Area theaters
BOTTOM LINE Branagh’s new Agatha Christie adaptation is a classy thriller for intelligent adults.

There’s a fine line between classic and cliché, and Kenneth Branagh’s Agatha Christie movies know how to walk it. The first, 2017’s “Murder on the Orient Express,” felt like an old Hollywood back lot production, a little stilted but appealingly dreamy. The second, last year’s “Death on the Nile,” was a heaving melodrama that would have impressed Michael Curtiz or Douglas Sirk. With the third, “A Haunting in Venice,” Branagh turns to the supernatural chiller and, by not reinventing the genre in the slightest, delivers another winner.

Here's the gloomy palazzo where a wealthy girl met a horrible end. Here’s the distraught mother, Rowena Drake (Kelly Reilly, “Yellowstone”), who summons a celebrated medium, Ms. Reynolds (Michelle Yeoh), to contact the deceased. And here’s Branagh himself as detective Hercule Poirot, he of the sparkling eyes and totemic mustache. Though retired, Poirot has agreed to observe Ms. Reynolds’ séance at the insistence of an old friend, Ariadne Oliver (Tina Fey), a mystery novelist always on the hunt for a new plot. Branagh and Fey make an appealing buddy couple: American sass meets European weltschmerz.

There’s a murder, of course, and so Poirot locks the massive iron doors and starts grilling the suspects, who include the superstitious housekeeper Olga (Camille Cottin), an ambitious young restaurateur named Maxime Gerard (Kyle Allen) and the mentally unstable Dr. Leslie Ferrier (Jamie Dornan). While piecing together clues, Poirot begins to hear voices and see faces that — to Ariadne’s amusement — he cannot rationally explain.

With “A Haunting in Venice” (based on a lesser-known Christie novel, 1969’s “Hallowe’en Party”), Branagh has officially established something that’s been missing from the movies: a franchise for discriminating adults. These films are decidedly old-fashioned, relying on top-notch actors, intelligent dialogue (by Michael Green) and sumptuous production (the sets are a mix of real Italian locations and England’s Pinewood Studios). The Christie brand comes with a certain literary integrity; Branagh brings the filmmaking craft. Call it Hollywood entertainment for the “New York Review of Books” crowd.

At the same time, “A Haunting in Venice” could be suitable for younger (though not too tender) viewers. Unlike your “Saws” and “Screams,” the movie never gets truly bloody — there is an impalement, but seen in shadow — and unlike the new wave of “elevated” horror, it doesn’t traffic in troubling taboos. A bespectacled, be-suited little boy named Leopold (Jude Hill, Branagh’s “Belfast”) seems designed to bring in young fans of Wednesday Addams: When we first see him, he’s peering at the adults over his hard-bound copy of Edgar Allan Poe.

With its tried-and-true scare tactics and highly complicated mystery — you’ll never solve it — this movie could have become trite in the hands of a lesser filmmaker. Instead, it feels like an early Halloween treat. Branagh is so comfortable in this genre that his Poirot even risks a little joke about figuring out “whodunit.”

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