Fans of the unfilmable novel must be having a terrible time of it now. In the last three weeks alone, two of the most notorious examples have made their way to screen. Admittedly one – Amazon’s Good Omens – functions as a pretty watertight argument for never trying to adapt an unfilmable book. But the other is Catch-22, and that functions as an equally watertight argument to the contrary.

I have to admit that I didn’t see this coming. Throughout its gestation, the Catch-22 series seemed like an almighty act of hubris; as if Hulu, still drunk on the success of The Handmaid’s Tale, went out of its way to adapt an even more knotty work. Catch-22’s unfilmable reputation came about in part because someone did try to film it once, in the form of Mike Nicholls’ 1970 feature, and the results were patchy at best. A similar fate of smug, too wacky mediocrity seemed inevitable.

And yet somehow they have pulled it off. The Catch-22 series is successful in almost every way. It is beautifully shot, thoughtfully written and incredibly well acted. It takes plenty of liberties with Joseph Heller’s book – there are approximately 25 fewer characters, almost no flashbacks and the ending is entirely different – but, having seen the series, I have come to the conclusion that these changes are exactly what make it sing.

I’ll try to stay clear of spoiler territory, but the biggest decision made by the film-makers was to break the book apart and put it back together in the right order. The book hops about all over the place, leaping from viewpoint to viewpoint and back and forth through time. It’s a terrific sleight-of-hand – when Heller decides to fill in the blanks caused by this literary restlessness, it comes as a punch in the guts – but it would have made for an incredibly annoying TV show.

Instead, the series takes its time to wear down its protagonist, bombardier John Yossarian (Christopher Abbott). His downfall is parcelled out carefully along the way, and each new attempt to escape his fate brings about new and awful consequences. By the time he is finally broken, it has a feeling of inevitability that wasn’t present in the novel. It also reinforces the notion that Yossarian is a classic antihero, rather than a sane innocent trapped in a world of madness. Every time he tries to wriggle free of his commitments, he causes something terrible to happen to someone else. When this happened in the book, everything was rationalised through prose. Without that safety net, Yossarian quite often just comes off as a dick. Perversely, this makes him a little easier to understand.

A classic antihero: Christopher Abbott as John Yossarian. Photograph: Philipe Antonello/Hulu

Speaking of prose, another smart decision was to avoid Heller’s tone as often as possible. The book is a smashed Rubik’s cube, full of repetition, circular reasoning and busted logic. All the characters are trapped by their own thought patterns, which is fun to read but – as anyone who has watched every episode of the tonally similar W1A can attest – can be brutal to sit through. It still happens here and there, so the doctor’s explanation of insanity is thankfully still intact, but it isn’t quite as punishing. Stripping the plot back and rebuilding it in the shape of a classic drama feels like a something of a masterstroke.

Especially compared with Good Omens, which suffered enormously from how faithful it was to the book. I don’t know anyone, aside from those falling within the very highest percentile of Terry Pratchett fandom, who didn’t groan in despair when Amazon’s adaptation opened with several minutes of arch narration over what seemed to be a deliberate copy of QI’s opening titles. Catch-22, less in thrall to its fans, is much more confident in its ability to take on a new shape, and this makes it far easier to watch.

It also feels more open-ended, as if Hulu has already entertained the idea of lengthening the series out beyond the source material. Let’s hope that the failure of the last two Handmaid’s Tale seasons is enough to put them off. However, if this was always intended to be a finite six-episode retelling, then Catch-22 might just go down as the first time that anyone has successfully filmed an unfilmable novel.

Catch-22 airs Thursdays, 9pm on Channel 4