It's ironic that the half-Jewish Gwyneth Paltrow is so often cast as a wet-dream Wasp. Here, she plays an uptown drifter who finds herself in Brooklyn, where she captures the heart of an anorak-wearing, Jewish dry-cleaner (Joaquin Phoenix).

Her yellow tresses glow delicately in the urban gloom. She’s as tall as a giantess; her breasts (she exposes one of them) are exquisite. Michelle and Leonard are neighbours, yet they seem worlds — nay galaxies — apart.

Business as usual, then, for Gwynnie. What makes this romantic drama intriguing is that Leonard, it transpires, is a delusional, bi-polar wreck. You don’t have to be crazy to obsess over shiksa blondes, implies director James Gray. But it helps.

Walk The Line star Phoenix is extraordinary in the lead, by turns infantile and sophisticated, contorted and bold. Leonard’s attempt to woo Michelle with a spot of antiquated breakdancing is a must-see. His horror when she turns away — ecstasy instantly replaced by emptiness — is just as convincing. Phoenix — still only 33 — looks almost middle-aged; his stale skin and raddled mouth are perfect for the role.

Leonard’s parents (the excellent Moni Moshonov and Isabella Rossellini) are determined to set him up with a nice Jewish girl called Sandra (Vinessa Shaw). She tells him that she works for a drug company called Pfizer.

Leonard, wincing, says that he’s familiar with the firm. They then have a conversation about the merits of The Sound Of Music. She admits it’s her favourite film. He shrugs, suddenly relaxed: “Yeah. It’s under-rated.” The script is full of such naturalistic epiphanies. It also contains wry laughs and subtle clues. Why does the attractive, sane Sandra seem so willing to take up with Leonard? Watch her apparently avuncular dad and you begin to suspect that Leonard is the first gentle male she’s been exposed to.

All of which makes Two Lovers infinitely more interesting than Gray’s previous collaborations with Phoenix (the desperately noir-ish The Yards and We Own The Night). Yet this remains a good, rather than great, film.

Gray says he watched Vertigo repeatedly before the shoot. If so, he failed to learn the right lessons. We want to connect with these characters, but increasingly contrived plotting keeps us at arm’s length. Leonard yearns to take risks. It’s a shame Gray didn’t take more.