The threesome have just released their sixth album, Let It All In, which has been produced by their pal, Elbow singer Guy Garvey.
It's tipped to take them to even bigger things, a status they'd deserve after 14 years as a band.
"I'd rather have it this way than being the next big thing," says drummer Andy Hargreaves.
"I didn't quit my job and start playing the drums properly until I was in my 30s, and I'm glad that success didn't happen when I was in my teens because I'd probably have ruined it.
"We really appreciate it, we don't take it for granted. There's also the worry that if we ever did become super successful we'd alienate our fan base.
"I do like the fact we've got a hardcore following and we're their special band."
2010's Sky At Night long player was an elaborate affair, with the band going for a more epic sound.
It resulted in a Mercury Music Prize nomination, and was also the first time the band had worked with Guy Garvey and Elbow bandmate Craig Potter, who they've been friends with for years.
But Andy doesn't think it'll be possible for Kloot, who play Oran Mor on Tuesday, to follow Elbow's long road to fame, where they became arena megastars after years of toil.
"It's amazing what's happened to Elbow, and we're so proud of them," says Andy.
"We're a completely different band though, they've tailored music for that [pop success] but I can never imagine us getting anywhere near that. It'd be nice to get a little slice of that though-"
Andy can't praise the work of Guy as a producer highly enough. He believes that because they're friends it means the Elbow lads know how to get the best out of the band.
"When you're going into an enclosed space with a stranger you've no idea how that's going to work," he says.
"A lot of a producer's job is psychology, in getting the best out of people.
"He's a really good cheerleader, Guy, he really understands how we tick. It's a bit scary going in with someone you don't know, and they put us at ease – we'd argue more if they weren't producing."
There's a traditional element to I Am Kloot, and how they approach songs.
They focus on the album as one body of work, rather than flinging songs on there in any order, and Andy isn't concerned by the number of people who prefer to only download one or two songs from a record.
"People don't listen to albums as they used to," he explains.
"They don't even download the whole album, but it's important to us that it feels like there's a Side A and a Side B, that it's a journey that takes you along.
"One of the hardest things for us is the running order, because the oddest things can be integral to an album.
"People might then cherry pick songs, but that's irrelevant to us."
The group also had the chance recently to pay tribute to a music milestone, when they contributed a cover to a re-recording of the Beatles' debut album Please Please Me.
The album has been covered by a host of acts for a Radio 2 special tonight, meaning there's some diverse names working with the trio.
"It's a funny old thing, I can't imagine how they chose us, or Mick Hucknall or the Stereophonics, it's all very strange," adds Andy.
It's not bad having that variety, and anything that celebrates the music is a good. We're doing Chains, which wasn't even written by them, it was written by Carole King and Gerry Goffin.
"It was very 60s, all 'baby baby' vocals. We're going to change all that-
"Johnny Bramwell is a big fan of Paul Weller, who's also doing it, as he loved the Jam when he was a kid.
"I don't know about doing collaborations though. Maybe Mick Hucknall and Johnny, that'd be a mad one-"
After years in the studio there's also an enthusiasm from the band to get back out on the road again.
However, for Andy it means the first lengthy time away from home since the birth of his daughter, which leaves him with mixed emotions.
"I'm a bit scared of it, I must admit," he says.
"There's pros and cons to it – when Elbow go on tour I think the ones with children are on the bus first as they want to get away for a bit! But we've never been away for long time, and I know I'm going to miss her.
"One of the benefits to what I do is that I get to spend a lot of time with her, and it looks like this year we'll be spending a lot of time in a van instead. But that's life!."
n I Am Kloot Oran Mor, tomorrow, 7pm. Sold out,