How about Bj?rk?

Put a Ringo on it! You probably heard of her since she did a duet with Hikki. And you like Shiina, you're bound to like Tokyo Jihen as well.

Shiina Ringo:

Kabukicho no Joou

Gibbs

Koko de Kiss shite

Honnou

Marunouchi Sadistic [I'm just putting it up here because it's one of my favorite songs from her. xD]

Yame ni Furu Ame

Shiina Ringo - Shuukyou

Meisai

I Won't Last a Day Without You [ft. Utada Hikaru]

And then there is BONNIE PINK. Her earlier music could be describe as soft, acoustic rock with blues and jazz thrown in. Though her later works are a more "pop" and upbeat. Unlike many Japanese lyricists, she is quite direct and simplistic.

Orenji [This song is ancient. xD]

It's Gonna Rain

Heaven's Kitchen

Do you Crash?

Kingyo

Daisy

You Are Blue, So Am I

Tonight, the Night

Last Kiss

Private Laughter

So Wonderful

A Perfect Sky

I been listening to Regina Spektor lately and to put it plainly, she's quirky and her music is brilliant.

Fidelity

Samson

Eet

On The Radio

That Time