The group bring their fourth record, Radlands, to Oran Mor tonight.
It's inspired by American life, and the band spent time in Texas working on it. But it was a strange experience all round.
"We were living in this old house out in the woods, so we were quite isolated," explains singer Blaine Harrison.
"There was insane stuff happening there – I think the house was haunted.
"There was a really strange bedroom which had a kind of chill in it. It was what used to be a child's room and it creeped us out.
"When I slept in there I suddenly got really ill for a bit and couldn't get up.
"There were all these strange paintings in the house, too – it was very Stephen King.
"But it's good to freak yourself out, and I hope some of that haunting quality might have got on to the record."
The band has usually been known for a bright, poppy sound on albums such as Twenty One and Serotonin, but Radlands is a slower-paced, more thoughtful record that takes its cues from all sorts of American culture, from the roots rock of Sister Everett to The Ballad Of Emmerson Lonestar's country flavour.
It represents a shift in thinking for Blaine, and he's glad the band decided to challenge themselves.
"Pop is definitely not where we are at the moment," he says.
"We're more interested in telling stories and making more intimate sounding songs.
"I still love pop music though, we all do, and at some point I'm sure we'll return to writing about girls."
The switch in style might have worked a treat, but the rest of the recording wasn't so smooth.
Aside from their haunted house capers, the band weren't sure they were doing the right thing by shaking things up, and that meant they were terrified of listening to the record.
"It's good to have a danger element when making music," says Blaine.
"It allows mistakes to happen and you can find yourself in a dead end. However, getting out of that can make for a really interesting song writing process, and there was a lot of that in Texas, a lot of scratching our heads and thinking 'What are we doing here?'
"We went out without a producer - which was the first mistake. So we had dug ourself into a hole, but getting out of that can be brilliant."
There have been other changes, too.
Bassist Kai Fish recorded a solo album last year and, unsurprisingly, then chose to leave the group once Radlands was finished. He's been replaced by Pete Cochane while the current tour sees them playing with pedal steel guitarist Matt Parks as well.
"It's Mystery Jets Mark 3, really," explains Blaine.
"The first incarnation was with Henry, my dad, who played on the first album, then it was the four of us and now it's a bigger band.
"It was hard to deal with Kai leaving as he was like a brother, so we couldn't replace him in the traditional sense.
"It feels like a different group now and the songs sound different now, because there's five of us playing them live. Who knows, on the next record there might be 11 of us-"
The Oran Mor crowd will just have to settle for the five of them, as Blaine gets ready to return to a venue that he's enjoyed playing in the past.
"We've played Oran Mor before, years ago, on an acoustic tour and that was great," he says.
"I love playing Glasgow, it's a very cultured city. There are good cafes, and what I like about Scottish crowds is that if they're not enjoying it they will boo or leave, but if they're into it they'll start dancing.
"They're responsive and that's great. English crowds aren't so responsive in that sort of way."
And the band has no plans to take it easy after this tour, as they're already looking ahead to another album.
"We have a bunch of different ideas, but a lot of them get bashed back into the ground after a while," adds Blaine.
"We'll see what ones come to fruition, but there will definitely be something in the early part of next year."
lMystery Jets, Oran Mor, tonight, 7pm, £14.