There’s nothing about the cream linen suit Jake Gittes wears in the opening scenes of Chinatown that suggests he’s a private eye. It’s 1937 Los Angeles, and he’s showing graphic photos of a couple having sex in the woods to a distraught husband, but Gittes is just a string tie away from looking like a wealthy plantation owner.

For a guy whose job it is to dig up dirt, he seems awfully clean—and for a guy whose working-class client can’t pay him, he seems pretty flush. He has a nicely furnished office with three employees, drinks coffee from a china cup and saucer, and drives a shiny new convertible. No schlubby trench coats for Jake—he’s always in three-piece suits (double-breasted, with belt backs, pleats, and perfectly coordinated pocket squares), expensive Florsheim shoes, and, of course, a fedora.

Later, hints about his past come to light—he used to be a cop in Chinatown, and it’s implied that he stumbled across and maybe tried to expose some corruption there. Whatever it was, it seems, it ended his association with the law. I like to imagine that he quit the force in disgust, but that he was savvy enough to sell his silence for a tidy sum.

Now he makes an honest, if not exactly innocent, living stalking cheating spouses, like Hollis Mulwray, a top official with the Los Angeles Power and Water Department.

Hollis’s wife, Evelyn, is as incongruous a femme fatale as Gittes is a private eye. A glacial beauty with sharp cheekbones and razor-thin eyebrows, Evelyn is partial to mannish suits and never shows much skin. She’s wearing a turtleneck the first time she appears and the closest she ever gets to cleavage is a slice of sternum revealed by a deep v-neck. The only time we see her legs she’s wearing jodhpurs and boots for polo, and there’s nothing come-hither about them. Like Gittes, she sticks to neutrals; the costume palette is so desaturated, you could almost forget the movie was filmed in color.

Chinatown won an Oscar for costume design—which is maybe an odd distinction for a film shot so closely that you almost never see the actors’ legs, but not an undeserved one. I won’t spoil the mystery, but it’s a complicated knot of real estate fraud, water rights, murder, and incest. The further Jake and Evelyn get pulled into the case, the darker their clothes seem to get. By the end, she’s in black and he’s in dark gray. And they’re back in Chinatown.