Cat Power, Queen Elizabeth Hall, London

On record, Cat Power's extraordinary music can seem a few notes away from not being music at all, so sparse is its production and structure. Her songs can be mantra-like and repetitive, or disjointed, structurally incoherent, her voice seemingly an ethereal resonance.

Cat (real name Chan Marshall, born in 1972, in Atlanta, Georgia) gives the listener the impression they are mainlining her emotions. Discovered in the early 1990s, she's attracted a growing number of devoted admirers, tantalising them in live appearances, hidden behind a Ramones-like fringe, and apparently on the brink of falling apart.

So there's a sense of relief when she wanders on stage and smiles at the audience. She begins playing, in her half-strummed, half-picked style, a battered Danelectro guitar that looks like it's been languishing in a dusty attic. Her astonishing voice sounds as though it has come from the same place, its deep-South country-twang combining a whisper with a growl. She introduces nothing, tending to play medleys of songs, or just fragments; "He War" (from her most recent record, 2003's You are Free), for instance, is stripped of its powerful chorus.

Power's guitar playing is ridiculously rudimentary: there are even moments when it a song is interrupted as she laboriously forms a barre-chord. She finishes a stint on the instrument with "Good Woman", then makes a "that was dodgy" hand gesture, and gives a thumbs-down - but the audience is entranced.

The piano allows her accompaniment to be even more minimal. Some songs are played with one hand: if she uses both, she can still fail to construct a chord. Once again, she merges songs, almost perfunctory with some gems. The beautiful "Names", for instance, is almost lost in a segue: a poignant list of adolescent contemporaries, a bit like a reverse "Abraham, Martin and John", its effect is diminished by the lack of space Power affords it and yet, strangely, that of the overall performance is not.

Power's simple two- and three-chord songs work like old blues: a repetitive musical figure overlaid with confessional vocals. "I could stay here and be someone better," she sings in the lovely "Colors and the Kids".

Typically, though, she deconstructs the song and tantalises us by not giving it a proper reading. By now, she seems to be having fun. She even, briefly, plink-plonks the "Pink Panther" theme, hissing "sorry" under her breath after every excursion. "I could play this one for four hours," she says at one point. This is true of almost every song she does: they could all last four hours, four minutes, or 40 seconds.

When she launches into her version of "Satisfaction", there's a cheer of recognition. She finishes with another fragment of "He War" and then she's off, meandering around the stage in coquettish, flirtatious appreciation of our applause. For the first time, I wonder how much of the shyness is an act. It's the first genuinely wrong note of the evening.