There is no shortage of young American groups producing lo-fi garage-pop, but only Best Coast are fronted by Bethany Cosentino. She gives the Los Angeles trio's debut album, Crazy for You, its achingly romantic slant – but it's on stage in front of a sold-out crowd that her value is really evident.

Despite looking the part – mismatched shorts and top, scuffed-up guitar – she's no cookie-cutter indie girl. No sooner has the first song of this short gig scratched and scraped to a close than she's talking about her cat, Mr Snacks, whose photo is on the album sleeve – there are totebags with his picture on sale outside – and showing off freshly manicured nails: "I got them done with the American flag, 'cos we're going home in two days." A kind of indie-budget Katy Perry, Cosentino is droll, confident and so indisputably the centre of attention that her bandmates – guitarist Bobb Bruno and new drummer Ali Koehler – just let her get on with it.

Musically, there's only one mode tonight. With no bassist, the sound rattles and quavers, but that's fine for songs that are essentially three-minute rockets of lovelorn venting. Though Cosentino is romantically linked to a member of another voguish band, Wavves, you would never know it from the bruised throb in her voice on the likes of Wish He Was You and I Want To, the latter a weepy girl-group pastiche. The unlucky-in-love theme is further developed with a cover of the Ramones' I Wanna Be Your Boyfriend, but she pulls herself together with the rancour of So Gone – a punk thrash-out inspired, she tells us, by Courtney Love. A thoroughly entertaining set from a star in the making.