Pop stars who complain that fame has cost them their privacy should look to Norah Jones, whose 28m record sales have barely dented her anonymity. She slips into the room for this Radio 2 show with supreme lack of occasion - the un-superstar dropping in to play a few tunes from her new volume of sleepytime pop. She spends most of the show tucked behind a grand piano, surrounded by the Handsome Band, whose task is to plump out her small, husky voice with a cushion of easy- listening jazz and country.

"This is weird cos it's so small," she marvels, as well she might, since tonight's audience - of a mere 250 - would comprise about 1% of a normal Jones gig crowd. "I can see every one of you - so if you yawn, I'll know."

Predictably, the word "yawn" provokes an overwhelming desire to do it, which is terribly rude in the face of such sweetness. If only she weren't so confoundedly relaxing. Hank Williams' Cold, Cold Heart becomes a pastel lullaby, and the creases are smoothed out of Tom Waits' The Long Way Home, while self-penned material from her enormously popular debut, Come Away with Me, idles along serenely.

This is the artist EMI hopes will put the oomph back into its share price - the optimistically titled new album, Not Too Late, is the label's key winter release. Previewed here, it offers a ray of light to shareholders: Jones has fashioned another tunefully intimate lifestyle-pop release that, by rights, will accessorise almost as many record collections as the first two albums. The funny thing is, over the course of the show, it starts to sound rather wonderful. While she sings, it's hard not to feel that things are pretty much all right.

· Broadcast on Radio 2 on January 27 and on BBC1 on January 28.