"Sometimes I'm sad and sometimes I'm angry," Rachael Yamagata says, with considerable understatement, before diving into a song from "the angry half". If this half-Japanese songwriter from New York is known for one thing, it's emotional frankness: she is one of those people who, when asked how they are, will tell you. And tell you. Tonight, she offers a lengthy explanation of each number, and the various heartbreaks that inspired most of them.

Tonight, she is more composed than she was at her 2005 London debut, when she treated the audience to a self-abasing analysis of her failed relationship with British songwriter Tom McRae, but her rambling introductions still give the impression of a person with one less layer of skin than most of us.

Despite taking four years to follow up her first album, Happenstance (a staple on the likes of The OC), Yamagata has a fierce London following, who greet numbers from the new two-part album, Elephants/Teeth Sinking Into Heart, with rapture. Rightly so: she absolutely cuts it as a performer. When she gets stuck into a song, crooning into a microphone with fairy lights woven around its stand, she becomes powerful. Her voice is smoky, her guitar-playing delicate, and she sings about vulnerability and loss with the certainty that the bumps in the road will be worth it in the end.

Yamagata has a lot of jazz in her voice, and her band - guitar, drums, strings - complement it, creating drifty moments when it would be perilously easy to nod off. Nobody does, because there is something compelling and demanding going on up there, with a singer who has been away too long.