On July 15, 1997, one of the 20th century’s most perversely awful convergences of fate occurred in Miami’s South Beach: Standing outside his mansion, superstar designer Gianni Versace was shot to death by Andrew Cunanan, a young man who’d recently achieved his own ghastly celebrity as a serial killer on the lam.

Titled The Assassination of Gianni Versace, it’s a fitting subject for season 2 of Ryan Murphy’s American Crime Story. The show’s first season, The People v. O.J. Simpson, elevated rubbernecking to an art. This, too, is a juicy saga, both outrageous and tragic: Cunanan’s murderous, three-month spree was senseless, sensational and scary — he all but rampaged across the headlines — and his suicide as authorities closed in left fundamental questions about his motives and his psychology unresolved.

This Crime Story’s power and significance, though, arise less from violent suspense (which it has) than its nuanced sensitivity to the fact that the murderer and most of his victims, Versace (Édgar Ramírez) included, were gay. Assassination operates like an enormous tuning fork that vibrates in response to the waves of tension that undermined gay existence across America in the 1990s.

Does the show go so far as to suggest that Cunanan, like Matt Damon in the 1999 movie The Talented Mr. Ripley, became a cold-blooded killer because of homophobia? Well, no. But this was still an era in which the acceptance of gay identity, internally and outwardly, was a fraught, paranoid business.

The closet was not an incubator of good mental health.

However, let’s return to the more exciting topic of violent suspense.

Assassination, based on Maureen Orth’s Vulgar Favors, oscillates between the luxe and the gory, but its nine episodes (eight of which were made available for preview) naturally focus more on Cunanan (Glee’s Darren Criss). If Cunanan were somehow able to be resurrected today, he might very well post his murders on Instagram under the insane notion that he was some kind of influencer — he was obsessed with celebrity media, and seems to have wall-papered his demented mind with images of fashion magazines, Rodeo Drive brands and A-list celebrities.

But romantic delusion (and disillusionment) may have been what triggered his killings: When the man Cunanan considered love of his life, architect David Madson (Cody Fern), didn’t reciprocate his feelings, he fixated on a mutual friend, Jeffrey Trail (Finn Wittrock), a former Navy lieutenant, as his rival and obstacle. Both Madson and Trail ended up dead, the first by gunshot and the second by claw hammer.

Assassination slowly works backward from the Versace murder, Cunanan’s fifth and final killing. Episode 8 even stretches all the way back to Cunanan and Versace’s boyhoods in Italy and on the West Coast, respectively. We have little Gianni, whose dressmaker mother respects and encourages his designing talent, and little Andrew, whose Filipino father, a fraudulent stockbroker, spoonfeeds him lies about wealth and privilege. Gianni sketches. Andrew reads Brideshead Revisited and chooses “Après moi, le dèluge” (“After me, the deluge”) as a quotation for the high-school yearbook. Gianni, hard-working and blessed with genius, establishes a world-recognized label. Andrew, good-looking and glibly sophisticated, becomes a gigolo to some very rich sugar daddies in San Diego.

Generally, though, being a kept man is not much better than being a kept dairy product — the expiration date comes soon. And so it happened with Cunanan.

Unloved, unsuccessful and increasingly untethered, was he jealous of Versace? Possibly. That would make this something like a serial killer’s Amadeus, with Cunanan as an especially crazed Salieri to Versace’s Mozart.

Still, none of this makes Cunanan comprehensible or, when all is said and done, pitiable. Otherwise, this might be In Cold Blood for fashionistas.

That said, it’s hard to gauge how well Criss’s performance works in such a tricky, diabolical role. He bears a striking physical resemblance to Cunanan, but he hasn’t been directed in a way that suggests the profoundly ambiguous core — admittedly, an oxymoron — of this man who could be both a smooth, adept dissembler and, as a killer, such a blundering, bloody improviser. To say that the surest approach to a character like this is sick humor — Christian Bale in American Psycho or even Kathleen Turner in Serial Mom — doesn’t mean it’s always the right way.

What places this Cunanan in the show’s broader context, and rather ingeniously, is his intuition of how he functions as a gay man, constantly calculating how much of himself he can safely risk revealing — how much he can get away with not as psychopath, but as a man. Pressing David Madson to be his accomplice in disposing of Jeff Trail’s body, he tells him not to call the police: “They hate us, they’ve always hated us. You’re a f–.”

We’re also reminded, painfully so, that Versace’s decision to come out of the closet with an interview in The Advocate had the potential to ruin his business (according to Orth, he was HIV-positive). Trail leaves the Navy in despair — here, we see him come close to hanging himself — because of its brutal, institutional bigotry. The FBI, questioning Versace’s lover Antonio D’Amico (Ricky Martin) after the murder, can’t quite grasp what a gay man’s “partner” would be. Even the old sugar daddies seem wary of anything outside their rich but circumscribed circle.

It’s a long way here from here to Call Me by Your Name.

Review: The Assassination of Gianni Versace Is a ‘Juicy Saga’ That Explores Celebrity Obsession