In pop, the word "troubled" is normally followed by "Pete Doherty", but it's also being applied to the allegedly on-the-edge nightclub chanteuse Madeleine Peyroux. Apparently prone to disappearing when she's had enough, she did just that during a tour last summer, and had to be tracked down by a private investigator. Tonight, though, the New York singer was in the mood to play ball, kicking off early and sailing through a long, demanding show.

There was little here to justify the stories that she finds success a trial. Months of touring her breakthrough album, Careless Love, have bestowed a poise that masks any qualms about fame. Her only quirk was a trickle of enigmatic comments ("We all came from far away, and we came from further than this ... just a strange thought") but it's in a jazz singer's remit to be odd.

Elegantly moving from the smoky swing of Dance Me to the End of Love to a defiantly plucky take on Dylan's You're Gonna Make Me Lonesome When You Go to the ghostly Weary Blues, she ticked all the boxes, and beyond. She even threw in a love song to her occasional Paris home, J'ai Deux Amours, sung in such fragrant French that only a native would have been able to tell whether there was any Brooklyn in the fruity mix.

Peyroux's only failing is that she's a muso at heart, willing to indulge long, long solos from her five-piece band. She listened pensively - my, that was a twitchy 10 minutes from the double-bass bloke - only rejoining a song when each player had exhausted himself. Here's where I'd have applied the ruthless hand of commercialism, confining the band to a strictly backing role. But that wouldn't be Peyroux, so cymbal solos seem a small price to pay.

· At the Royal Concert Hall, Glasgow, tonight. Box office: 0141-353 8000.