Time For a CD Player Upgrade

Didn't hear anyone mention vibration control. Not sure what your CD player is sitting on, but vibrations affect CD players (along with turntables) the most out of anything and I bet (regardless of your surface and flooring) you would benefit greatly from a Townshend platform or podium combo or Symposium's rollerblock Jrs, or some other brand (I only have experience with those companies). There are low level earthquakes going on all the time that you can't feel, but your equipment can.

I was amazed what it did for my turntable so much that I took care of my phono stage and amp and speakers (speakers were also a very highly use case with platforms and rollerblocks where they fit best).

@nonoise  - I don't like worrying about positioning that type of vibration control - too much playing around with positioning and spring (or the like) tension. I recommend either a platform that has the springs locked in like the Townshend seismic one, or the Rollerblocks I mentioned that are solid and dissipate vibration inside the component and isolate it from outside ones via ball bearings inside two solid discs that absorb the vibrations.

Some who take it to the extreme even put the roller blocks under a platform for extra vibration treatment. I had to do a double treatment on my turntable - a wall shelf with a Townshend platform sitting on top of it. The Townshend actually created footfalls because of the springs, so adding the shelf eliminated them (as per Max Townshend himself-RIP - a kind of mad scientist). It was either that or don't use the Townshend, but that cleaned up the sound so much that I was going to either tread lightly and live with the footfalls or put the table and platform it on a wall shelf. Luckily the boss didn't object to the wall shelf in our den.

Also, solid platforms with multi layers can work well. Depends on the application and component. I use them for my speakers because I didn't want them to be bouncing around.