Originally Posted by Joliet John

Actually, it is exactly what you should do. It is the basis for headlight restoration kits. You have to remove the damage using an abrasive. If the damage is heavy, you can start with 800 grit. You move up to finer grits to get rid of the sand scratches. You can buy a kit from 3M for a bit over $300 - it includes two tools (one for sanding, one for buffing), several grits of sandpaper, a couple of different compounds and buffing pads.

The part I disagree with him on is clearing over before you've buffed out the 2000 grit sand scratches using compounds. Being a headlight, you'd want to have the lens as smooth as possible (to avoid diffusing the light). You should have it looking awesome - polished and clear, when you finish with the compounds. The clear coat is to replace some of the UV protection you've just ground out of the lens.