Need to clean some cds

I found just the stuff!
Meguiars "Scratch X"
Automotive car finish fine scratch and swirl remover.
It does wonders to TT covers.
And cleans off scratches on Cds too. (I HAVE used it on CDs)
Most important: the cloth you use must be 100% cotton and SOFT!!! Even go and buy a new thick 100% cotton Teen/girls stretchy tee shirt and cut it up for rags. (The 100% cotton stretchy thick fabric of this sort of tee-shirt is perfect)
Brand new 100% cotton socks can work also

I'll second the Meguiars "Scratch X".
I have had great success with it.
The best cloth to use is a BRAND NEW baby diaper.
Doesn't get any softer that that.
I use them on my classic car.
Just my $.02.
Rick.

Do you wipe from center to edge of each CD (or in circular motion as with vinyl record) when rubbing out scratches on a CD?

My usual method is to wash the CD first in room temperature water, then pat dry. (get any dust off, and tiny specks of "scratch-ola" off too!)
I polish with tight oval motions from the rim to the center and back, not just perfectly straight back and forth, and proceed around the CD with the rubbing ovals until back at the start... etc. So it is a steady motion, not a jerky motion... like spirals, not zig-zags.

Power tools, you need power tools my friend.
Seriously, doing anything to the CD's will only make them sound worse. Polishing one area will made the surface wavy- not a good thing. And any scratch removing polish will put in zillions of finer scratches.
You could try Novus #1 which puts a shine on CD's. Or Armor All. Just make sure you wipe off the excess so it doesn't spray around the inside of your CDP. Also clean the center ring area of the CD. I use saliva since it's plentiful and easily accessible. Otherwise the disc may slip due to the slippery surface oils and not drive correctly.