Over the last five years, The Bad Plus has been one of the hottest bands on the jazz circuit. The group has also been among the most controversial.

Few jazz fans would doubt the chops of pianist Ethan Iverson, bassist Reid Anderson, and drummer David King; all of them have played wonderfully in more traditional settings. But when they get together in the hyper-power trio that is The Bad Plus, something happens.

Sure, they might occasionally tackle a jazz standard - but you might not recognize it. They're better known for the pop songs they dare to lift into the jazz ether. On the band's latest album, "Prog," the musicians interpret David Bowie's "Life On Mars." Past albums have included renditions of Nirvana's "Smells Like Teen Spirit" and Blondie's "Heart Of Glass."

And this band is not a good choice for rocking the baby to sleep. It fills the stage with energy and an over-the-top style of playing. Young people tend to love it; purists run in the other direction.

Pianist Ethan Iverson was on the road with The Bad Plus when we spoke to him by phone. The following is an edited version of our conversation.

City: When strong jazz personalities get together, there's always unique chemistry as they react to each other. But when you three combine it seems like a special kind of magic. What do you attribute this to?

Iverson: Reid and Dave have been playing together for over 20 years, since they were 13 or 14. They grew up in the same suburb of Minneapolis, Golden Valley. I was couple of years younger but I met them when I was still in high school. We formed the band in 2000, but the roots go back to the late 1980's.

Possibly what you're sensing is that this is actually a band of three leaders, something jazz could use more of. Rock is better at that. It's not like a different bass player is going to show up and play one night. The Police were those three guys; that's definitely our attitude. The Bad Plus are these dudes who are equally invested in what happens. In jazz there's too much of a star soloist showing up with whoever in the rhythm section.

Who are your strongest influences?

In terms of piano, Thelonious Monk and Keith Jarrett. I am a pretty voracious listener of jazz. The whole world of Ornette Coleman and the whole world of John Coltrane are really important. But it ties into what I was saying earlier: the Coltrane I really love is with McCoy Tyner, Jimmy Garrison, and Elvin Jones. And the Ornette Coleman I love is the band with Charlie Haden, Dewey Redman, and Ed Blackwell.

I hear echoes in your playing ranging from Chopin to Don Pullen.

I love Chopin and Don Pullen, for sure. I do know something about classical music. That is an element in The Bad Plus, along with indie and electronica. We try to let it all in.

You seem unusually interested in dynamics. On your latest album you go from Don Pullen-like pounding on "Physical Cities" to the hushed, subtle bass on "Life on Mars."

We're not about restraint in The Bad Plus. We're interested in extremes - extremely soft, extremely loud. We want it to be bold. We play with the kind of intensity associated with rock. It's not a rock band, but at the same time there's a sort of really digging in that jazz people can sometimes sort of skate around when they play in a rock style.

Your repertoire is also unusual. "Chariots of Fire," "Everybody Wants to Rule the World," "This Guy's In Love With You" - how do you choose tunes?

The first time we played a cover was the Nirvana song. On our first gigs we'd all written our own music but we didn't have enough to play two sets. Jazz musicians usually play standards. Dave and Reid had messed around before with rock music. I didn't know anything about rock, but they said, "Let's play a Nirvana song." So I thought I'd better learn it.

We rehearsed it and I immediately felt this has something. We tried to bring some of the real belief or attitude to it. We don't jazzify it. I'd never put a Bill Evans chord structure to any of those songs. The harmonic structure comes more from power chords on the guitar, or 20th-century classical music.

What's been the reaction to your choices from jazz purists?

Some jazz purists don't like it, and don't like The Bad Plus. We just do what we do. It's not a grand political statement. We just play the music we want to play. And certainly it's not a new idea. We regard as the jazz tradition to play the music of your day with improvisation.

Some of the same traditionalists worry about jazz dying. By playing today's music, you bring young people to the music.

Sometimes a 16-year-old will come up to me and say, "I didn't know I liked jazz. I'm going to have to check it out." If there is a way for The Bad Plus to get in there and warp some young minds, we're all for it.

In terms of original tunes, you have some pretty unusual titles. For instance: "Layin' A Strip For The Higher-Self State Line."

Dave, who wrote that song, likes 1970's films about trucking, like "Convoy." And he also believes in metaphysical ideas - that you should be as good a person as you can. So if you want to mix Buddha and Kris Kristofferson, you get that title.

With all of that energy on stage, how exhausted are you after a concert?

Sometimes that's when I feel really energized. I might have been tired during the day from traveling. I always get excited for the show. Then it's like I just did something that made sense of my life - let's party.