I think if you're pretty into Japanese artists, there's a good chance you've at least heard of Shina Ringo [椎名林檎] (or Shiina Ringo, or Sheena Ringo, according to iTunes). She's been on the scene for a few years now, though I only became aware of her a year or two ago. Her music is a bit varied; if I had to assign her a genre, I'd say punky jazz rock.
A few weeks ago I bought her album Kalk Zamen Kurinohana. I had listened to random songs of hers on YouTube before, but this was the first album I've bought, and I really enjoy it. It's definitely rockish, but quite mellow, too. If you're interested in picking it up, it's definitely a lot cheaper to buy it via iTunes if you can. Amazon Japan carries it at a slightly more expensive price, and Amazon.com has an import version that is quite costly.
Anyway, don't take my word for it - check her out. Here are a couple songs from Kalk Zamen Kurinohana performed live. These versions are a little more rocky and less mellow than the album verion, but I like both styles. I particularly like the lyrics of the first song and the kick-ass piano and haunting melody of the second.