Chirurgie Centrum Logo Concept

Working on a few new concepts for a new Dutch Surgery Centre.

Edit: for some reason importing this kind of Illustrator artwork into Photoshop causes some obvious gradient banding. I tried a few tricks such as Noise, Spatter, changing bit-depth, etc. But these seem to be a little bit too much for smaller artwork. Any of your Photoshop guru's know a neat trick to get rid of those gradient bands once and for good?