Alice Cooper was a big fan, but he never met Prince. He did, however, engage in a bit of push-and-pull with Prince over a fellow musician.

"The only real relationship we ever had was he kept trying to steal Orianthi out of my band," Cooper tells Billboard, referring to guitarist Orianthi Panagaris, who's also worked with Michael Jackson, Carrie Underwood, Dave Stewart and, most recently with former Bon Jovi guitarist Richie Sambora. "Every time I talked to Orianthi she'd be on the phone and say, 'It's Prince again.' I said, 'Could you tell him that you're with me for about the next year' -- kidding, of course. I know that he liked to have pretty girls in his band. Other than that I don't think I ever talked to the guy."

Cooper did, however, have "total respect for him. Nobody really got how good of a guitar player he was -- just a great, great guitar player. Musicians knew how good he was. I don't think the public knew how good he was, though."

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Cooper himself is stealing away a little time from his own band to work with Hollywood Vampires, the supergroup he and actor Johnny Depp formed for a self-titled, mostly covers album that came out last September. After playing a few shows last year, they have 22 dates in North America and Europe booked, starting May 24 in Verona, NY. "I was expecting to do five shows this summer with the band, so I'm pleasantly surprised," Cooper says. "I was like, 'Wow, how did we get Johnny away from the movie business for that long?' He's just decided he's gonna take that time off and do the Vampire thing."

The concerts will feature songs from the Hollywood Vampires album, including two originals, along with the new track "As Bad As I Am" that the group performed at the 58th Annual Grammy Awards. With Aerosmith's Joe Perry, Stone Temple Pilots bassist Robert DeLeo and former Guns N' Roses/Velvet Revolver drummer Matt Sorum on board, the shows will be kept "loose" in order to accommodate any musical friends who might want to join on a given night and won't have the same kind of visual theatrics as one of Cooper's concerts.

"I think that who's on stage is the show," explains Cooper, who calls the Vampires "a super bar band."

"I think you're going to see that a Vampires show, musically, is tight, but I think visually it's not going to be anywhere like an Alice show as far as this happens here, this happens there. I wanted to have some looseness to it. Even the makeup; sometimes I go back to the band and go, "Makeup or no makeup? You want me to be this Alice or that Alice?'"

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The Vampires are also planning to record another album, according to Cooper, this time getting away from the covers that populated the group's debut. "The next album will be all new stuff," says Cooper, who also has a new album of his own in motion including collaborations with original Alice Cooper band members Michael Bruce, Dennis Dunaway and Neal Smith. "We're already writing for the next album. I don't now what Joe's gonna bring. I don't know what Johnny's gonna bring in. I know there's three or four songs I've started writing for the next Alice album, and I've already gone, 'It doesn't work for our album, but that might work for a Vampires album,' which I think is a little more modern rock. It's still guitar rock, but it might have more elements of modern rock."