Plastic headlights are covered by a clear coat, similar to the clear coat on your paint.  When this outer layer oxidizes, you will see cloudiness..  This oxidation needs to be completely removed by using several grades of sandpaper.  We quite literally scratch our way to clarity..
Now we have an oxidation - free, but very scratched surface.  This surface is then polished in multiple stages with a high speed machine polisher.  After we achieve a clear, transparent finish, we seal the headlights with Ceramic Coating to prevent any deterioration from recurring..

It sounds like a lot, which it is.. But these steps are necessary to produce professional results and to PREVENT the problem from recurring.