Warm sounding power cord for for CD player to suppress digital glare on vocals.

Harry Pierson had an interesting observation years ago. He said that if you really wanted to enjoy digital, stop listening to your records. 

Here's a  move that will bring your CD playback up to a point where it's  really worthwhile ... replace all of the fuses in your electronics (and speakers (if applicable) with the SR Red fuses. I'm in awe over the major improvement in my CD playback with these little critters. 

Oregon, whether exotic fuses influence the sound really depends on the circuit design. In some circuits, it can make a substantial difference (eg: Ayon), in others; none (eg: Vitus), so you need to do your homework & talk to the manufacturer before laying down your hard earned quan.

Forget the power cable,put a Tube Buffer between components.You will never hear digital the same again & you will love it!

Wouldn't it be easier to just buy another CD player?

A Sablon Audio Robusto PC will definitely do the trick. It's an older cord that you can pick up for little money.
 It's not as detailed and open as newer cords but the tone is beautiful.