Joan As Police Woman, Barbican

Joan Wasser, who operates under the name of Joan As Police Woman, has probably seen all sorts in her time, having played with Antony Hegarty and Rufus Wainwright and dated the late Jeff Buckley. But even she was thrown by an inappropriate comment from the stalls at the Barbican last night. "Show us your tits" is the sort of thing female comedians in working men’s clubs, not soulful, passionate musicians in concert halls, have to put up with.

As well as that unexpected heckle worthy of the Frankie Boyle brigade, there were a number of issues at this gig which nearly derailed it. There were initial problems with Wasser's vocals being too low, which she blamed on "ghosts" messing with the soundcheck. Unusually for this pristine venue the acoustics were problematic, with some fans at the sides unable to hear clearly even after the volume was cranked up. Then when Wasser switched from Moog keyboard to guitar after two songs there was no power coming from her amp. Nerves also seemed to be a factor in a performance that stuttered, but hit the spot in the end.

So much for the downside; there was plenty of upside too. Wasser certainly cut a formidable figure in a black leather catsuit which evoked various reference points, from her namesake Joan Jett to Elvis in 1968 comeback mode, though I don't recall Presley wearing vertiginous heels for his famous televised gig. Wasser announced that she is planning to wear the same trousers at every show on this tour and expressed a hope that by the end they will be able to stand up on their own.

The music was never less than interesting of course, as she delivered a set mixing highlights from her new album, The Deep Field, with older songs that clearly still mean a lot to her. Fronting a cost-effective trio, this was a very different gig to her lo-fi 2009 visit. After a few emotionally turbulent years – and albums that reflected her roller-coaster life – Wasser is feeling decidedly upbeat. "Chemmie", given a welcome outing early on, for instance, is about pure lust: "So then we stopped this getting to know, and got to getting down".

Her backing musicians – Tyler Wood on keyboard, Parker Kindred on drums – mostly kept things sparse, particularly on the ruthlessly funky single "The Magic", which has a bouncy hook that really gets under your skin. This is a band that constantly finds new directions for familiar forms. Just as you think Wasser is turning into a female Muscle Shoals-era Al Green or a potentially bland cross between Duffy and Dusty Springfield, she often distorts her vocals and takes them in an expectation-subverting direction.

The experimental side is never too far away from her pop sensibility and worked very well throughout, except for the extended final pre-encore track "I Was Everyone" – apparently about Joan of Arc "from her perspective" – which sailed perilously close to Spinal Tap’s "Stonehenge" prog-rock territory with its key changes, psychedelic noodling and twists in tempo.

This, however, was a rare moment of sonic excess. Wasser's real strength is going for a less-is-more approach on showstoppingly minimal tracks such as “Anyone”, from her 2006 album Real Life, which prompted one of the biggest cheers of the night. Her voice was so raw and packed with emotion it was the most powerful instrument onstage by miles. Never was this better exemplified than on the very last song, a cover of John Lennon's “Woman”, which had a haunting, delicate beauty and reduced the audience to absolute silence. Even the phantom heckler could not come up with a response to that.