You can't win as an artist in the world of the Coen brothers.

In Barton Fink, a Broadway playwright's attempt to sell out to Hollywood led to writer's block and a descent into nightmare. In contrast, the folk-singing hero of Inside Llewyn Davis refuses to compromise his art. But he's still pretty luckless.

As artists themselves, the Coens get to have their cake and eat it, making impeccably individualistic films which are nevertheless embraced by the mainstream. Llewyn would be impressed with their integrity, while Fink would look on with envy, thinking: "How did they manage that?"

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Inside Llewyn Davis is one of their best, a sublime, bittersweet account of the struggles of a singer-songwriter to succeed in the folk revival in America, just before Bob Dylan arrived to shake the scene up.

It's 1961 in New York. In the famed Gaslight Café in Greenwich Village, Llewyn (Oscar Isaacs) is singing a plaintive, traditional folk song (as with all the songs in the film, it's performed in its entirety).

"It's never new and it never gets too old. It's a folk song," Llewyn tells the audience reverently, stepping off the stage to applause. Moments later he is beaten up in an alley by a man he doesn't know but has clearly offended. The next day he wakes up on someone else's sofa, with a cat on his lap.

This is Llewyn's life. Struggling to go solo after a failed double act, he is broke, homeless, sleeping on a different sofa every night. His agent is doing nothing to promote his records; when Llewyn asks for money, he is handed a box of his own unsold albums and a winter coat.

One of his regular couches belongs to a couple, fellow performers Jim and Jean (Justin Timberlake and Cary Mulligan). Llewyn has recently slept with Jean, and she's pregnant with his child, but she loathes him - Mulligan's performance is an enjoyable flurry of foul-mouthed vitriol. Llewyn, who has been in this position before, cheekily asks Jim, the ignorant cuckold, for money to pay for the abortion.

Llewyn also has uptown benefactors, whose enthusiastic support he resents, and whose cat he reluctantly finds himself responsible for. A wonderful sequence offers the animal's perspective of the New York subway; Llewyn's later pursuit of the pet through the wintry streets evokes the iconic album cover of The Freewheelin' Bob Dylan; the whole film is enthused with a wet, blustery, somehow gorgeous melancholy.

We follow the singer over the course of a few days. In one hilarious scene, he and Jim perform a comic curio of a song about President Kennedy; as soon as Llewyn demands the quick cheque rather than royalties, we know it will be a hit. On a drive to Chicago, where he hopes to audition for a producer, a drug-addled jazz man (John Goodman) taunts the younger man's folk leanings. Can it be coincidence that the brilliant Goodman was also Barton Fink's nemesis?

Self-involved, stubbornly refusing to compromise and increasingly resentful, Llewyn is not the nicest of heroes. Yet Isaac retains our sympathies with the purity of his playing and a beleaguered comic charm. He's a revelation in his first starring role, and the film itself a joy from beginning to end - and with a beginning and end which you need to pay keen attention to.