This is an excellent reason for upgrading the "source" (cd player, or turntable depending on the owners preference). If you had replaced the speakers first, you would have had a better sound of the output of your old CD player. Since you replaced it, we can assume you felt it bad and/or lacking.
With equipment of the quality you mentioned, you may want to look slightly higher in the Axiom line. That is if your space and budget allow.
Let us know how it sounds completed!