Darren Criss as Andrew Cunanan
CNN  — 

“American Crime Story” faced a daunting challenge in following up the compulsive appeal of “The People v. O.J. Simpson.” The result, “The Assassination of Gianni Versace,” carves out its own distinctive approach to another high-profile, salacious murder without, perhaps inevitably, wearing the mantle quite as well.

To their credit, the producers have demonstrated the format’s elasticity by delving into the 1997 slaying of Versace, the famed fashion designer, as part of a killing spree by Andrew Cunanan.

Working from Maureen Orth’s book “Vulgar Favors,” the narrative jumps around in time, filling in bits and pieces of the story out of sequence, in a manner that galvanizes attention and gradually builds in intensity.

The show’s point of view, however, unfolds pretty squarely from the perspective of Cunanan, a compulsive liar and hustler whose grandiose vision of himself and pangs of economic anxiety triggered his tragic behavior.

While Darren Criss (who previously teamed with producer Ryan Murphy on “Glee”) delivers a strong, compelling performance, the underlying efforts to humanize Cunanan and, indeed, explain him drifts down some troubling and questionable corridors. As Murphy’s projects often do, the effect at times risks not just providing insight into a murderer, but glamorizing him and his grisly actions.

Understanding what drove Cunanan is at the heart of the project, but “The Assassination of Gianni Versace” is frankly more notable for some of its smaller roles, and for what it says about the toll exacted by homophobia and being closeted during the 1990s, which contributed to the authorities’ slow response.

Cunanan, for example, pursues wealth through relationships with older men, whose skulking around to hide who they are actually makes them prey for a sociopath eager to exploit them. In that regard, the project is exceptionally well cast at the margins, including Mike Farrell and Michael Nouri as two of Cunanan’s benefactors, as well as Judith Light as Farrell’s oblivious spouse.

Versace’s family has already criticized the series, but his experience is actually dealt with far less expansively. Edgar Ramirez plays him, with Ricky Martin as his lover and Penelope Cruz a perfect choice as his protective sister Donatella, who endeavors to be the business-minded ballast to her brother’s artistic genius.

“American Crime Story,” of course, has been victimized to a degree by its own success. The latest edition premieres as practically everyone in TV has been drawn to the true-crime genre, both in documentary and scripted form.

The challenge, of course, is that while there are plenty of sensational cases out there to mine and adapt, only a handful of them have the immediate recognition and heft to justify eight or 10 episodes, much less the allure of the Simpson trial.

Viewed that way, allowing for the stated misgivings, the latest “American Crime Story” nimbly demonstrates the latitude that FX has to operate under this banner. And if it doesn’t rise to the same level as its predecessor in terms of racing through an airport to catch the next episode, “Versace” ultimately aces the watch-ability test with flying colors.

“The Assassination of Gianni Versace: American Crime Story” premieres Jan. 17 at 10 p.m. on FX.