"This is one of my favourite songs that Allison has ever written," says Catherine Pierce, the blond, guitar-free half of this Los Angeles-based soft-rock duo. Casting an inexplicably withering glance to her right, Allison replies: "You really built it up there." It's the kind of loaded sibling badinage that, if this were the Gallagher or Davies brothers, would be followed by flying microphone stands. The sisters, though, just glide into the next song, I Put Your Records On, and their voices melt together in silvery harmony.

That's the thing about the Pierces, whose 2011 breakthrough album, You & I, contained enough MOR top-coat to get their gothish folk-pop on to the radio after a decade of knockbacks. Whatever is going on behind the scenes, it's not played out onstage or in the music, which remains shimmering and harmonious. Their new album, Creation, seamlessly adapts the formula: a little less spook-pop, a little more gloss, but all bound together by the silkiest harmonies.

The setlist of their first UK tour in three years is dominated by Creation. "I hope you don't mind," apologises Catherine, the voluble master of ceremonies and lead singer – but what's to mind? While the new songs lack the noirishness of Love You More and We Are Stars, there's magic in the sinuously intertwined voices. I Can Feel brings out the Cranberries-esque Celt-rockers in them; the country-blues Believe in Me and Kathy's Song, sung a cappella, invoke their Alabama roots – something that could be fruitfully explored in more depth.

Less fruitfully, they cruise into Haim-style jauntiness on the recent single Kings, which Catherine confidently introduces with: "I think you're gonna know this". But the fans' squeals of recognition are saved for the show-closing 2011 hit Glorious, which so bewitches one chap that, after the Pierces leave, he continues to film the empty stage.

• At Koko, London, 11 June. Box office: 0870 432 5527. Then touring until 14 June.