Lenny Kravitz

By Mark Dagostino

05/21/2004 at 03:30 PM EDT

Fame, money, women – you'd think it would be all a rocker needs to get by, but for Lenny Kravitz, it's just too much. The musician – whose every hair style and clothes change is snapped by the paparazzi – sings "I Don't Want to Be a Star" on his new album, Baptism. "You miss the way it was before people were, like, hunting you," he says. But still, there are perks to being a big celeb. Kravitz (who's dad to Zoe, 15, with ex Lisa Bonet) recently chatted with PEOPLE about some of the pluses – including dating Nicole Kidman and living next door to Courtney Love.

Listening to this album, one might wonder: Are you happy?
Completely. That's what this album is about: becoming happy and accepting myself. I got a big ol' grin on my face.

How great is it to be in a band?
It's pretty awesome. Making music is it for me. But I do also want to have that partner and that home life. But, you know, it will come when it's supposed to come.

Speaking of that ... obviously there's a high-profile woman that you were linked with in the past year, Nicole Kidman ...
Who's that? Just kiddin'.

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How did you two meet?
We met online. No, I'm kidding. We just met through a mutual friend and we've become really great friends. And that's really where it is right now. She's somebody that I really respect and admire as a person.

Romance-wise, anything going on between you two now?
At this point, honestly, to tell you the truth, we're connected – no matter how you slice it. We have a connection. Right now we're great friends, and where it will go or not go, I couldn't tell you.