Darren Criss as Andrew Cunanan, the real subject of “Versace” Ray Mickshaw/FX

In the first scene of FX’s American Crime Story: The Assassination of Gianni Versace, the title character (Edgar Ramírez) wakes up, glides through his gilded mansion, accepts a glass of fresh-squeezed orange juice that he sips by the courtyard pool, and heads out to buy a stack of magazines from a nearby newsstand. This is the Nineties Miami of The Birdcage, a haven for gay men, awash in creams and peachy pinks. The second installment of the true-crime anthology series that Ryan Murphy began with The People v. O.J. Simpson, Versace tells another blood-soaked story about the crazy-making quest for wealth and fame — or at least the appearance of it.

At the outset, The Assassination of Gianni Versace, which premieres January 17, feels like a straightforward continuation of The People v. O.J. Simpson, which also takes place in the mid to late 1990s. Both examine the then-novel concept of death as a 24-hour-news-cycle spectacle: When Versace is gunned down in front of his home, a crowd forms outside, and a tourist who earlier sought the man’s autograph now sneaks under police tape to dip a Versace ad torn from a magazine in the designer’s blood. But it’s fitting that the show opens on the last morning of Gianni Versace’s life, on July 15, 1997. By the second episode, Versace himself fades from focus, replaced by 27-year-old serial killer Andrew Cunanan (Darren Criss) — a nothing, a nobody, until he made a name for himself by murdering his idol.

Criss’s portrayal of Cunanan, a gay man whose outward confidence and taste for the finer things belies a deep well of insecurity, is the highlight of the show. This is a guy who can make eating a bowl of Froot Loops look menacing. The gripping performance is enhanced by the show’s narrative structure, a risky gambit that pays off: The season moves backward in time, each episode taking place just before the events of the previous week’s. Versace is a puzzle the viewer puts together as it goes on, and with this approach the story seems to ripen with every episode as we move deeper and more intimately into Cunanan’s past.

We also learn about his other, less glamorous victims, almost all of them gay men who entered into relationships with Cunanan. (The series is based on the 1999 book Vulgar Favors: Andrew Cunanan, Gianni Versace, and the Largest Failed Manhunt in U.S. History by Vanity Fair’s Maureen Orth.) Writer Tom Rob Smith, himself openly gay, draws out the way Cunanan exploits the stigma of being gay in the 1990s both to lure his prey and to cover up his crimes. He is devious in his manipulations. Against his victims, Cunanan wields a possessive logic: The world doesn’t want or accept you, but I do. Against law enforcement, he cannily exploits the systemic straightness of police, leaving behind evidence of the victims’ sexual proclivities that makes it easier for the cops to, if not dismiss the crimes, treat them with a smirk and a sideways glance: Oh, it’s a gay thing. “They hate us, David. They’ve always hated us,” Cunanan tells an ex-boyfriend. “You’re a fag.”

Versace is not camp; it’s a respectful and often deeply moving depiction of the struggle for acceptance, both from the wider world and from oneself. Despite the boldfaced names touted in FX’s ads, the story of Gianni Versace, his sister Donatella (Penélope Cruz), and his lover of fifteen years, Antonio D’Amico (Ricky Martin), merely frames Cunanan’s escapades. Thematically, the parallel storylines of Versace and his killer work in tandem: In one episode, we witness Cunanan construct a sellable version of himself as Gianni helps Donatella design her first dress; in another, Gianni contemplates a public coming-out while the alternate story follows a gay character in the Navy during the era of “Don’t Ask, Don’t Tell.”

The Versace family has already released a statement declaring the show’s depiction of the late designer’s professional and domestic struggles a fantasy. But the Versaces are the embroidery here, not the tapestry. Like Orange Is the New Black’s Piper Chapman (Taylor Schilling) — the nice white lady who’s sent to the big, bad prison — the Versace angle is a Trojan horse, a mass-marketable hook for a series that’s actually most interested in stories about less flashy, more marginal characters. This is far less a show about a fabulous atelier than it is about a handful of gay men you’ve probably never heard of.

Sure, it’s a bait and switch. But maybe that’s what we need at a moment when a powerful speech at an awards ceremony is all it takes for the press to begin breathlessly anticipating Oprah 2020. As much as I loved O.J., which rightfully won the Emmy Award for Outstanding Limited Series last year, I have serious reservations about the prospect of our popular culture being clogged with stories about celebrities from twenty years ago (next up on the Murphy/FX docket is Feud: Charles and Diana).

The casting of the long-closeted Martin as Versace’s partner is a nod to the fact that we have finally reached a point where an openly gay man can create a show for a major cable channel that’s this, well, gay. With so few straight characters, Versace can move beyond the anxiety of representation — no one gay man stands in for the whole. There’s no hint of a character or storyline that feels wedged in for the sake of the platonic straight male viewer. Cruz is wonderful as the fledgling version of the Donatella we know and love — and also, it has to be said, almost distractingly beautiful — but she remains fully clothed throughout.

Again, it’s Criss who is the main draw. Despite a bit of mid-season sag in the plot, he holds the viewer tight in his grip. Cunanan exerts control over his victims calmly, which is so much scarier than bluster, like your mom going real quiet when you know you’re in trouble. He’s got a Trumpian swag, an unearned confidence in his ability to sell himself to anyone. And yet Criss never lets us forget Cunanan’s desperation and shame, the self-loathing just beneath the surface of the collegiate bravado. You can just make out the panic behind his eyes. “You can’t go to America and start from nothing,” Cunanan’s father, an immigrant from the Philippines, tells him in a flashback episode. “That’s the lie.”

The character calls to mind two creepy-brother portrayals in films of the past year: Caleb Landry Jones in Get Out and Billy Magnussen in Ingrid Goes West. Like this pair of privileged yet sinister bros, Cunanan as depicted in Versace is a country-club psycho — an embodiment of the moral rot at the core of the pristine image of the American dream.

American Crime Story: The Assassination of Gianni Versace premieres January 17 on FX.