Not long ago, the members of groove-surfing New Zealand seven-piece Fat Freddy’s Drop set themselves a strict new rule: No more jamming.

Currently working on a follow-up to last year’s “Blackbird” album, the group had discovered that there’s such a thing as being too creative. With each studio session yielding yet more new material, founder Chris “Mu” Faiumu decided to “put his foot down” and demand some collective restraint.

“Actually, we all kind of had to put our foot down,” says trombonist Joe Lindsay, speaking via Skype from his home in Wellington. “It’s like: We need to work on these songs. We’re not allowed to jam any new ones.”

There are worse fates to suffer than a surfeit of ideas, but it might help explain why the band has produced just three full-lengths in its 15-year career.

“Our album process is quite long and drawn-out, so you’ve kinda got to get it started reasonably promptly if you want it to come out this century,” deadpans Lindsay.

In this era of Tumblr, Soundcloud and canny viral marketing campaigns, the story of how Fat Freddy’s Drop made it sounds positively old-fashioned. Emerging on the Wellington live scene in 1999, the group started out as what Lindsay describes as a “high-powered, improvised ensemble that didn’t record,” peddling a freewheeling blend of dub, soul, house and funk.

“We got more popular, and built up a reputation through live performances and word of mouth until people were clamoring for an album,” he continues. “And we thought, ‘Oh, we might as well record now.’ ”

That album, “Based on a True Story,” went straight to the top of the New Zealand charts when it was released in 2005, and today the group can claim — without a trace of hyperbole — to be the country’s biggest-selling independent act, ever.

So how has Fat Freddy’s Drop managed to avoid coming to Japan in all this time? Despite seeming like a shoo-in for one of the larger stages at Fuji Rock Festival or Summer Sonic, the group’s show in Tokyo this weekend will be the first time they’ve ever played here.

“Yeah, it’s funny,” says Lindsay. “We’ve spent a lot of time concentrating on Europe. We’ve been through the States a couple of times, but we’re such a big group, we kind of need to go where the going’s good, really.”

You can see the point. Last month, the band played its largest-ever gig in the U.K., a sold-out date at the 10,000-capacity Alexandra Palace in London. Daikanyama club Unit, where Fat Freddy’s appears under the Red Bull Music Academy banner on Saturday, is going to seem a little cozy in comparison.

And while they’re eager to make up for lost time, don’t expect them to play their biggest hit. Lindsay explains that the group ditched 2005 single “Wandering Eye” from its repertoire after the song became too ubiquitous in New Zealand.

“Every cafe we went to, it’d be playing, so we had to give it a rest for a while,” he says. “The whole idea of having a hit song, for us, was always a bit embarrassing.”

Fat Freddy’s Drop plays at Unit in Shibuya-ku, Tokyo, on Nov. 8 (11:30 p.m. start; ¥3,000 in advance; 03-5459-8630).

In line with COVID-19 guidelines, the government is strongly requesting that residents and visitors exercise caution if they choose to visit bars, restaurants, music venues and other public spaces.

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