When Adam Green announces that a song is so old "it should be in a museum", you have to remind yourself that, although he's still only in his early 20s, he's the veteran of something like six albums, and has been a star of New York's Lower East Side demi-monde since he was a teenager.

He obviously has a thing for Jim Morrison: close your eyes during new single Nat King Cole and his nimble band could be the Doors. Classic bobby-sox rock'n'roll fires more than a few songs, too, the band swinging hard as Green orchestrates an unabashed, old-fashioned good time.

He's prolific, but the songs are short: 24 zip by in barely more than 70 minutes. Green is a shambolic presence, an often bewildered-seeming child-man, but unequivocally a star; baby-faced but possessed of a rich, low tenor that's as potent as diner coffee. There are times when the gleeful obfuscations of lyrics that combine bizarre gynaecological aphorism with what would probably have once been called hipster jive can seem merely glib games. But just as you are thinking this he will hit you with a line that cuts through it all, singing about "a boy who built a snowman out of himself" or "I can't go home without going home with you" in a forlorn monotone at the end of Computer Show.

"Sometimes I think if I could just please this one man," he says as someone in the crowd calls out for a song - then a perfect comic pause, "My father." He's playing, of course, but maybe he isn't, returning to the subject later with similar gallows humour. This, perhaps, is Green's genius, the way little moments of emotional truth leak out almost by accident, wrongfooting you. Maybe his heart has been there on his sleeve all along. "There's been a lot of bad talk about a lot of bad stuff," he says, unexpectedly, summing up the evening before the encore. "Now I wanna sing something encouraging."