18. The Ladykillers (2004)

What on earth was this about? A remake of the Ealing crime-caper classic (with Tom Hanks in Alec Guinness’s crackpot mastermind role) at least proves, if proof were needed, that the Coens have excellent cinephile taste. But this was pointless and baffling. A case of No Coen Do.

17. Burn After Reading (2008)

What a dog’s brunch of a film: a strained and unfunny black comic gang-show of big names, with one or two good gags and an admittedly intriguing turn from Brad Pitt as a dopey fitness freak.

16. The Hudsucker Proxy (1994)

This period Capraesque comedy about an ordinary guy – a rather uncharismatic Tim Robbins – who is elevated to corporate greatness as part of a share-price scam is an example of how the Coens’ comedy can sometimes lack focus: too quirky and spongy.

15. O Brother, Where Art Thou? (2000)

The Coens’ love of Preston Sturges resurfaced in this film that whimsically takes upon itself the title of the desperately serious social-realist movie being planned in Sturges’ 1941 Sullivan’s Travels. It is an appealing, likable film about three runaway chaingang convicts in depression America who pass themselves off as a bluegrass trio, their record somehow becoming a hit. Silly, amiable stuff that has faded with time.

14. Hail, Caesar! (2016)

More golden age Hollywood nostalgia with this cantering comedy about tinseltown: the boozers, the fixers, the divas, the hoofers, the scribblers. It features George Clooney as a none-too-bright ageing star in a cheesy toga-wearing Roman epic. The movie reminded the world what a great dancer Channing Tatum is.

13. True Grit (2010)

Unprecedented commercial success was what the Coens found with this handsome remake of the 1969 John Wayne classic; or rather a new adaptation of the original novel by Charles Portis. Jeff Bridges was probably the only possible casting as the no-account “Rooster” Cogburn, with Hailee Steinfeld as his employer, the 14-year-old Mattie Ross. It is a good-natured, well-made movie, but perhaps without the strong taste of the original, or the Coens’ other films.

12. Intolerable Cruelty (2003)

Here is the biggest “underrating” issue in contemporary Coenological studies. On release, most critics seemed to decide that this screwball divorce comedy with Catherine Zeta-Jones and George Clooney was no good. I disagree. The smoothie lawyer Miles Massey was a part Clooney was born to play, and Zeta-Jones’s cat-that-has-every-intention-of-getting-the-cream predator is tremendous.

11. Raising Arizona (1987)

Some Coenoisseurs regard this early comedy as one of the top three; maybe even the gold medal. For me, it doesn’t stand up that well, but it is an utterly distinctive film with twang and snap, a realist-fantasy action comedy drama with weird subplots and extraneous minor characters. Holly Hunter is the cop who falls in love with Nicolas Cage’s criminal; on discovering they can’t have kids, they get involved in the most wackily innocent child abduction imaginable.

10. The Ballad of Buster Scruggs (2018)

The Coens have created a gem with their latest film, a western portmanteau of tales from a comically picturesque old west, conceived with humour, warmth and visual flair. Some stories are better than others, but the best are superb, and Tim Blake Nelson has what must be the greatest role of his career as Buster Scruggs, the singin’, gunslingin’ cowpoke.

9. Barton Fink (1991)

This was the award-winning movie that turned the Coens into hall-of-famers, a fantasy satire of golden-age Hollywood about a lonely screenwriter called Fink (John Turturro) mixed up in a horrible mystery. There is a fair bit of early-90s style-over-substance, and the film was denounced by no less a figure than Arthur Miller as “meaningless”, but stylish is undoubtedly what it is.

8. Inside Llewyn Davis (2013)

The complacent world of early 60s pre-Dylan folk is the location for this touching and often hilarious drama about a failing Greenwich Village folk singer: the prickly Llewyn Davis (that Welsh-sounding first name does not in fact exist outside this film), played by Oscar Isaac. It is a poignant look at the awful midlife decisions that artists have to make when it becomes clear that their careers are not working out.

7. A Serious Man (2009)

The big debate about how funny the Coens ever fully intend to be is maybe crystallised by the adjective in the title here: an entirely engrossing and personal film, set in the mid-west of their childhood. It is wonderfully acted by Michael Stuhlbarg (an all too rare lead role for him), who plays the academic plunged into despair when his wife declares that their marriage is over.

6. Miller’s Crossing (1990)

An inspired prohibition mob thriller that has been alchemised into a Coen film with an elegant and eccentric comic perspective. There is a great performance from a young Gabriel Byrne as that gangster-staple: the ambitious young guy in the organisation, a little out of his depth. And there is a glorious shootout soundtracked by Danny Boy.

5. Fargo (1996)

One of the Coen movies to be garlanded at Cannes, this comically inflected noir is now enjoying an afterlife as a TV spinoff. Frances McDormand gives what may be her greatest Coen performance as Marge Gunderson, the pregnant Minnesota cop investigating a crooked scheme by William H Macy’s car-dealer to kidnap his own wife.

4. The Man Who Wasn’t There (2001)

Discussions of the Coen oeuvre always centre on what’s over- and underrated, and there is plenty of room in the closely grouped mid-table for this kind of argument, but for me The Man Who Wasn’t There is one of their very best films: an eerily beautiful and slow-moving black-and-white LA noir in the style of James M Cain or Robert Aldrich, with Billy Bob Thornton as a barber whose wife (Frances McDormand) is having an affair with her boss (James Gandolfini). Gripping.

3. Blood Simple (1984)

The Coens’ devastatingly good low-budget debut from 1984, an inspired noir thriller, quite without the comic quirkiness of their later works. It still looks and feels entirely original, despite its obvious generic inspirations. Frances McDormand is a young woman, cheating on her abusive husband (a superb Dan Hedaya), who then hires a creepy gumshoe to follow her,with a showstoppingly evil performance from M Emmet Walsh.

2. The Big Lebowski (1998)

For many, this will always be the greatest Coen film, and it is certainly beguilingly funny, baggy, freewheeling and strange, with a great performance from Jeff Bridges as the Dude, bringing a weird gravitas to a role that might have seemed merely spacey or wacky with a lesser performer.

1. No Country For Old Men (2007)

This sensational and apocalyptic drama, based on the western thriller by Cormac McCarthy, is still the Coens’ masterpiece: a noirish nightmare that takes place under a vast Texan sky, leavened with brilliant wisecracks. Javier Bardem’s Anton Chigurgh is a horribly bizarre villain, and Tommy Lee Jones’s sheriff is a voice of sanity and humour in a world of evil.