If the scratches are deep but on the other side, I find a good long hard rub with metal polish, finished off with a really good wash in hot soapy water, thorough drying & finally a polish with a silicone furniture polish works well. Try and keep the polish and soap away from the hole in the middle, because if it gets in there, it gets stuck between the laminations and gradually eats away at things.
It does make the entire surface a little duller at the same time as disappearing the deep scratch, but this is partially rectified by the silicone polish & usually doesn't stop the disc playing in a half decent player.
I find those 'CD cleaning kits' you can get in bargain stores etc, the ones that contain a tiny bottle of isopropyl alcohol and a spinning jenny, are utterly useless unless the damage & dirt is so minor as to not affect playback anyway.
Next time my 4 year old destroys a postman pat CD I'll give the silver paint trick a try as well, thanks! I've binned my fair share of what I thought were completely unrecoverable disks because of label side scratches.