Them Crooked Vultures singer Josh Homme.

Them Crooked Vultures have their priorities straight.

“This is something special and it’s important to try to keep it that way,” says singer-guitarist Joshua Homme of his newly minted supergroup with Led Zeppelin bassist John Paul Jones and Nirvana drummer Dave Grohl. “We don’t want to ruin a good thing.”

And so far, it’s been a very good thing. Less than 16 months after their first jam session, the impeccably pedigreed power trio have taken the rock world by storm. Their self-titled debut album — which deftly fuses the three musicians’ talents into a sum greater than its parts — topped rock charts in Canada and the U.S. and earned solid reviews, while their hot-ticket live shows have been described as “pulverizing” and “ferocious.”

As the band prepared to head north of the border for a handful of dates this month, the 36-year-old Homme (it rhymes with Tommy) called me from his Palm Springs kitchen to reveal the secret to their success, his dreams of competitive Rubik’s cubism and his love of unsafe music.

Are you surprised at everything that has happened in the last 15 months?

Yeah. Our world — both as three guys and the world in general — is moving so fast. I’m often surprised by it. And we really haven’t done that much. We haven’t over-toured. We’re playing one week a month, basically.

Why?

From the get-go, the idea was that this should be something a little more mysterious, frankly. Ideally, it should be something that a bunch of people want to see and just don’t get to. The idea isn’t to pound pavement to make sure we get everywhere twice. If anything, we would rather play half the places once.

I presume that keeps it fresh. But don’t you have to keep scraping off the rust?

Yeah, but that’s the fun part; finding a new way to scrape off the rust. We know how to do this Rubik’s Cube. But we want to do it under the lights of Rubik’s Cube competition. Whoa — I’ve never used that one before. That’s got a visual, damn it.

Your album came out less than six months ago. Are you already sick of being asked when you’re making another?

Yeah, but partially it’s of our own making. We mentioned the idea once in New Zealand and it just took off. And we do want to make another album. But it’s important to not pressurize a situation like this. So we haven’t spent any time trying to be Nostradamus about it. But we really want to. We know we’re going to.

Have you got past the stage of glancing over at Jones and thinking, ‘Holy f---, that’s a guy from Led Zeppelin.’

No. And I hope I never do. I always look over and say, ‘What a badass, man.’ This is something that has yet to stop exciting me.

Do people in the audience shout out requests for Zep?

Somebody did one time. I think it was for No Quarter. I just said, ‘This is not a cover band.’ But I gotta say, since the very beginning, there’s been something very special between the band and its audience. We asked them to take a leap. We did a tour without any record in sight, and played a lot of new music to consume in one show. We said, ‘Will you trust us? We promise to try as hard as possible.’ And we’ve had the most giving, trusting audience. To have only heard No Quarter one time — and it was in jest — is really amazing.

Jones must have some incredible stories.

The funny thing is, as we were recording, we’d each be sharing stories and talking. And it would dawn on me, ‘These are Zeppelin stories.’ But really, they’re stories about his friends who just happen to be Zeppelin. And the humanizing of those characters has really been kind of tender and cool for me. But yeah, the stories are crazy. (Laughs)

You’ve always had a lot of oars in the water — Queens of the Stone Age, Eagles of Death Metal, producing. Are you happy being monogamous with this, or are you getting itchy?

Well, Queens is playing the Reading and Leeds festivals in England in August. But in general, I love the brothel mentality of music — the Caligulesque version of music. The benefits of playing with other people — and then taking that learning and creativity back to your home base — cannot be overlooked. I just think musical safety equals death — and this is a great way to be unsafe.