How do you remove film from plastic headlight covers for BMW?

I have the same problem with my Lexus ES300 (bubble-eye). I just used some "straight" ammonia on a rag and wiped it. It still has a film, but not as thick.

OR.

# Step 1 Squirt a half dollar sized dollop of scrubbing cleaner, such as Liquid Comet, onto one of the towels. Scrub the outside of the headlight housing thoroughly. # Step 2 Rinse the scrubbing cleaner off with the soapy water. Polish until it is completely dry. # Step 3 Soak one corner of the second towel in plastic polish, such as PlasticX. Polish the headlight with a circular motion until the polish is completely rubbed into the headlight. This will fill in any scratches that have caused dullness and brighten the headlights up more than just dirt removal will. # Step 4 If the headlights still appear dim or discolored, remove the headlight housing. Clean the inside of the headlight glass the same way as you did the outside.