Try T-cut, I've used it on a valued Steve Reich CD which was scratched by my car autochanger and it works fine on my CD transport now. Follow up with something like Reveel.
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I have been using Meguiare's plastic polish for years on my cd's and it works very well. It takes a lot of arm work but the end result is very good. You can find it at most auto parts stores in the wax aisle. Also a company named Novus makes a plastic polish and it seems to work the same but with a lot less effort.