i found out that what really works for hazy/dirty headlights is clay + meguiars plastic cleaner + wax

 

as driguez mentioned, meguiar's plastic cleaner does a good job of removing haze. I just use Meguiars dual action cleaner/polish (DACP) because it was convenient for me.

Klasse AIO or Meguiar's Scratch-X work as well.

Keep a layer of wax on the headlights and it will be easy to clean.