The five-piece play their first Scottish show this Sunday at Stereo.
They are on the rise in part due to the vocal style of frontwomen Holly Laessig and Jess Wolfe, who tend to jointly sing every line in their tunes, rather than have one of them take lead.
With a musical backdrop that sometimes calls to mind Phil Spector's Wall of Sound, and at other times goes towards folksier material, both women's voices still come through loud and clear.
"We were always mesmerised by that Spector sound, the sound of the 60s where everyone was doubling their vocals for the first time," recalls Jess.
"We thought it would be interesting to recreate that in a live setting, so it was a happy accident. We both wanted to be lead singers but together and we didn't want to just be doing harmonies."
Holly and Jess have been friends for around a decade, and been playing music together for most of that time.
They met while studying at the Berklee College of music in Boston and hit it off straight away.
After years spent gigging together as a two-piece, they decided to expand their sound, adding drummer Dan Molad at first, with guitarists Peter Lalish and Andrew Burri following soon after. That led to their debut album Wildewoman, which has earned comparisons from classic 60s pop through to Arcade Fire and Haim.
The group's songs, though, owe a debt to the shared connection between Jess and Holly.
"We are best friends, so it's easy to pin the songs as coffee talk," says Jess.
"I know what's going on in her world and she knows what's going on in mine, so when we get together it's easy to bounce ideas off one another.
"We have experienced many things in a parallel kind of way, with love and loss - we can relate to one another because it's oddly happened around the same time."
If the lyrics suggest a bond between the two friends going back several years then the music on Wildewoman was much more spur of the moment.
JESS insists there was no grand plan to make an album when they headed into the studio.
"We all got together, but not really with a goal in mind," she says.
"We were just throwing spaghetti at the wall and trying to develop something new, because Holly and I were mainly doing slower, folkier stuff before that, and we were ready to advance."
One aspect of the band they were much more sure about was how they should look - their onstage appearance, with matching outfits, has marked them out on the fashion pages as well. "It's important that the band isn't just a bunch of individuals, but that you're seeing a unit," says Jess.
"We get into the same headspace when we are onstage and that look connects the dots for a lot of people.
"We call it dressing the sound, but it's a lot of fun, and a lot of the acts we love, like Bowie or the Kinks, their look went hand in hand with their music and you can't imagine one without the other."
There's no plans for any outrageous Lady Gaga style outfits, though.
"Everybody hopefully has a purpose for what they are doing, and as long as you have got a purpose for what you are doing then great," she adds.
"It might not be what I would feel comfortable doing, but if somebody feels sexual and wants to express that in what they wear then I'm not going to stand in the way of that."
There has been one problem to their growing success, though - they have had to cancel plans to stay in Scotland for a few days and have a holiday after Sunday's gig because of a TV opportunity.
"We are very much looking forward to going to Scotland," says Jess.
"We would actually booked a three-day adventure after our show in Glasgow, we were going up to the Highlands and then going to Stirling for a day too, but we have had to change the whole schedule as we got booked on Jools Holland show.
"We are a touring band, that's where we thrive, when we can connect with an audience, and I'm just excited to be experiencing all these countries for the first time."
n Lucius, Stereo, Sunday, £7.50, 8pm