How do I get rid of the thin artifact outlines around my live paint fills?

The first screenshot shows the wireframe view (CTRL+Y) in Illustrator. The second screenshot shows the normal view in Illustrator. The white artifact lines are very thin, but still visible. The third screenshot shows the pasted result in Photoshop, scaled down. When the drawing is scaled down in Photoshop, the outlines become more evident and make the design look really bad.
This is what I've been doing:
- In Illustrator, I used calligraphic brush to draw the outlines of my character.
- Converted the whole character into a live paint group.
- Filled in my character with the live paint bucket.
- Copy and pasted the character as pixels into Photoshop.

