I used Meguiars Clear Plastic Cleaner & Polish (PlastX) from Schucks on my headlights, $7.49 for a 10 oz bottle. Worked great for me. This is the description.
"This easy-to-use, rich gel formula quickly restores optical clarity to both rigid and flexible clear plastics. Cutting-edge advancements in Meguiar’s exclusive Microscopic Diminishing Abrasive Technology (MDAT) remove light oxidation, chemical degradation, surface contamination, stains and light surface scratches with ease. Special highly water resistant polymers provide long lasting durable protection to keep your clear plastics clear and beautiful longer. Meguiars recommends applying PlastX with a High Tech Applicator Pad or Ultra Plush Super Terry and using an Ultra Plush Super Terry or Supreme Shine Microfiber for the final wipe-off."