How can I improve my CD sound?

Every CD player is different. A laid back sound (What comes to mind first are Marantz SA-11s12? SA-7s1? SA-15s1?). Simaudio? Accuphase? Classe? Read some reviews and try to get a clue from that. Audition carefully. System synergy plays a real big role. Thanks

Bill

>>It takes the harshness away<<

Hardly.

Not all solid state is harsh/etchy and not all tubes are lush/warm.

>>and it sounds even better too.<<

Totally untrue.

Most of the best digital gear is solid state.

No question, CD is an unforgiving medium. It's takes attention to detail and a good player. Everything matters- power cord, interconnects, vibration control/isolation, demagnetizing discs before play, cleaning off the mold release, treating the surface...

Modest(average) CD players are very sensitive to AC noise incoming and also output digital noise which is very audible.
The beauty of FM broadcast is that you don't have the digital electronics of a CD player creating the digital noise into your system; and, many quality broadcasters have some form of AC conditioning(balanced power)for their systems.
Your CD player will be far more listenable if you use isolation/conditioning on the AC feeding it and will improve further if you do the same for your preamp.
Best wishes for improved sound, there's a lot of great music on CD.