I'm not sure if this is exactly the right place for my question, but here it is:

I'm creating a model for a client of a sphere made of jigsaw puzzle pieces. Several of the pieces will be missing, revealing a differently-textured sphere underneath. I've been messing with ways of accomplishing this without having to model the outer sphere directly, and I've achieved some good results so far with a combination of transparency maps and bump maps. The issue though, is that by using transparency maps to exclude the missing pieces from the outer sphere, the pieces have a very flat, two-dimensional look (like paper jigsaw pieces floating above the inner sphere). What I'd like to know is if any of you guys (or gals!) out there know an efficient way I can give them some thickness.

Thanks for the help!