Ive got me the Digital Nasties

Interconnect cables and the CD player power cords....
Also issolating and/or filtering the AC power to the CD player from the rest of the system.

In my experience, the AC cord is the first tactical move against digital nasties then come AC filtering.

Trying to manage your audio cables so it doesn't cross with one another especially with powercords is a freebie tweak that works too.

Other than cables, this recent thread is helpful:

http://forum.audiogon.com/cgi-bin/fr.pl?ddgtl&1051384332

Ditto above. Plus try adding RFI stoppers, AQ or Radioshack. to the CD players output cables.
One way to compare the sound is to run your Cd through a audiocassette deck. If the digital grunge sound dissapears, then attack you front end. if not, it's after the cassette.

Try placing Black Diamond Racing Mk. III cones (warmer than the linear Mk. IV) under your digital gear.