"You know why I joined the Air Force during Operation Desert Storm?" asks the gorgeous, eversmiling Alisa in Thin. "To lose weight!" It sounds like a line from The Devil Wears Prada. But the divorced mother-of-two isn't joking.

Like Shelley, Brittany and Polly, the three other Americans at the centre of this sublime, excruciating documentary, Alisa has a eating disorder that, on several occasions, has almost killed her.

Director Lauren Greenfield met these women at the Renfrew Centre, a Florida facility that attempts to get anorexics and bulimics back on track. You might expect the result (filmed over six months, with unprecedented access) to be an ad for the good work that goes on at Renfrew. But no.

There is a One Flew Over The Cuckoo's Nest element to Thin, and Southern diva Polly is its Randle McMurphy. Initially a star pupil, she is soon breaking the rules - no secrets, no cigarettes - with furious glee. She even pukes up (the ultimate Renfrew taboo) before our eyes.

By rights, Polly's story should end badly. And yet, by the time the credits roll, her situation appears the least tragic. Are all secrets bad? Is anger always destructive? These are just some of the questions provoked by a film that seems relevant not just to young, middle-class women, but anyone who finds " good behaviour" hard to swallow.

An interesting detail is that in the accompanying book Greenfield wrote about Renfrew, the issue of rape crops up constantly. In the film, Greenfield pushes her camera into a lot of sensitive spaces but, in terms of sex, the subjects are allowed complete privacy. Invisible, inaudible and respectful, Greenfield is the antithesis of film-makers like Michael Moore or Nick Broomfield. Different stories require different storytellers, but she was definitely the perfect woman for the job.

•Thin screens today. LFF runs until 2 November. Information: www.lff.org.uk; 020 7928 3232