Penelope Cruz’s bizarre portrayal of Donatella and outstanding acting by Ricky Martin were two of the more startling features that stood out in The Assassination Of Gianni Versace.

But, as with The People vs. OJ Simpson the reality the drama was based on was even stranger. The white dove found lying by Versace’s body, also killed in the shooting for example, was a detail the best crime writers couldn’t make up.

There’s one big problem with making a show as universally acclaimed and exactly right for the times as The People vs. OJ Simpson and that’s what do you do next?

The Assassination Of Gianni Versace was not just the perfect follow-up but arguably, amazingly, even better material.

It made similar observations about the downside of celebrity, the appetite of the media, and flawed police procedure and prejudice (sexual this time rather than racial) but was more glamorous, more intriguing, and revealing than the first American Crime Story mini-series – largely because most viewers knew the details of the OJ case/murder (the Ford Bronco chase, the gloves etc) beforehand.

In contrast, this had an assassin few of us knew much about, that (strangely) never became as famous as the likes of Mark Chapman or John Hinckley Jn, despite killing Versace and being wanted by the FBI for four other murders at the time.

Episode One suggested that instead of facts established by a court case and endless analysis in the media, the story here revolves around speculation and ambiguity.

Even the show wasn’t sure we could believe what we were seeing, or saying that we should.

The issue whether Gianni Versace had ever met his killer Andrew Cunanan before their fatal encounter on July 15 1997 is disputed by the designer’s family.

Here though we saw Cunanan approach him seven years earlier in the VIP area of a nightclub in San Francisco and subsequently meet him at the opera he had created the costumes for.

The various versions of how these came about (and whether they did at all) was a product of three sources: the book Vulgar Favours by Vanity Fair writer Maureen Orth who supposedly uncovered them; scriptwriter Tom Rob Smith who by the series’ own admission ‘filled in a lot of the blanks involving the relationship between predator and prey’; and anecdotes by Andrew Cunanan himself.

The problem was, as we saw, that Cunanan was an inveterate liar, a pathological fantasist, and seemingly a sociopath – unable to empathise with other people emotionally or understand why telling the truth even mattered.

‘Is it real?’ a friend at Berkeley asked him about the story of meeting Versace.

‘How do you mean?’ frowned Cunanan, genuinely puzzled. ‘Honestly, truthfully, I really do swear I have a date with Gianni Versace !’

Given the lies he’d told about being half-Jewish and his sexuality his friend (like us) found Cunanan’s claims unlikely.

‘You tell gay people you’re gay and straight people you’re straight,’ he pointed out.

‘I tell people what they need to hear !’ countered Cunanan gleefully.

Darren Criss (Blaine Anderson in Glee) was superb portraying Cunanan’s dual personalities: the American Psycho-styled loser with ‘nothing’, consumed by self-hatred, torment over his sexuality, and jealousy of Versace’s lifestyle also able to pass himself as a handsome, camp, student at UC Berkeley and then blend into Miami’s beach scene.

He was wearing a grey t-shirt, shorts, and ordinary orange baseball cap when he walked up to the designer and shot him in broad daylight outside his house on Ocean Drive.

Criss certainly had a whale of time depicting Cunanan’s derangement (mimicking the shocked response of a woman watching Versace’s death on TV, placing his hand over his mouth as she did – except to conceal his glee at the news), not to mention his chilling charm and penchant for elaboration.

‘For my first job I worked for my father on his pineapple plantation in the Philippines ! Can you imagine that?!’ he purred to Versace (supposedly), before claiming his father had also been a pilot for Imelda Marcos and that he was writing a novel about his ‘crazy’ family.

Edgar Ramirez was equally brilliant as Gianni Versace (not to mention eerily similar physically) but the contrast between characters couldn’t have been greater.

Every time Versace spoke about his childhood and his family, his stories were touching and admirable.

His inspiration was his mother’s ethos as a dressmaker and the Versace company logo (the head of Medusa) far from the crass, pretentious, symbol people regarded it but a memory of his childhood playing in Rome’s ruins.

‘For me family is everything,’ Gianni gently explained to Cunanan (again allegedly). ‘The first dress I ever made was for my sister Donatella. Maybe every dress I make is for her.’

Penelope Cruz as Donatella made a late entrance but predictably a drama one, descending from a private plane wearing trademark leather trousers and a huge pair of shades.

When she took them off she didn’t look much like Donatella, or sound like her (or even Italian) when she confronted Gianni’s partner Antonio D’Amico (Ricky Martin), dismissing his sobbing snapping: ‘that’s not what I need from you right now. You are not to speak about my brother without consulting me first.’

D’Amico had just been grilled by the police – the scene that showed most that the Versace story may lack the resonance of OJ Simpson’s but it still has a striking relevance to modern-day politics/prejudice.

Asking about the lovers and one-night stands Antonio arranged for Versace, one FBI officer wondered: ‘did they consider themselves to be his partner too? Do you see why I’m confused? What’s the difference?’

‘I lived with Gianni for 15 years. I was his companion not his pimp !’ D’Amico wept. ‘It’s a good length of time,’ conceded the Fed. ‘Were you paid?’

Cruz came into her own when Donatella declared she was cancelling her brother’s plan to float Versace on the New York stock exchange and intending to keep it in the family.

‘Gianni grew his company from one small store in Milan, from a single rack of clothes, a little simple bench,’ she reiterated to their lawyers. ‘This company was his life. My brother is still alive as long as Versace is alive. I will not allow that man, that nobody, to kill my brother twice.’

Admittedly her words (and her accent) were more reminiscent of a woman announcing she was taking over South American drug cartel than the heir to an Italian fashion empire.

Everything about her portrayal of Donatella right down to the styling was suitably flamboyant without ever necessarily being completely convincing.

But even this was a reason to watch, to see how it/she progresses, and part of what made The Assassination of Gianni Versace as mesmerising as its predecessor about OJ.

The Assassination Of Gianni Versace, by Jim Shelley