No, You need a High Speed Buffer to heat up the plastic and apply the non-abrasive compound or cleaner wax to now scorned area.

Steps to cure this problem:

1) clean the headlights (soap & water)
2) using 2000 grit sandpaper and a bottle of half/half soap and water....Wet sand the whole headlight on each spot (not just the problem spots)
3) clean the headlights (soap & water)
4) Using a High Speed Buffer (2800 rpm to 3500 rpm) carefully apply a few spots of cleaner wax such as Meguires.
Hold the Buffer wheel at an angle so only 1/4 of the pad is touching the surface, Press lightly on the buffer so the pad makes a good contact with the headlight and doesn't want to roll away.
Do not let the pad sit in one area for more then 3 seconds, Otherwise you have a chance of melting the plastic lense and now your fuct.
5) After you have seen a huge difference in clearity, Apply regular wax to the headlights, Let them dry....The you can use the buffer or hand buff the wax off to get a brilliant shine and a clear headlight.

G/L with the cleaning and hope this little step by step list helps you out.

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