I registered just to reply to this.
It's very easy to gain a great improvement, it takes skil to get them perfect.
Any polishing compound (chrome polish for example) will yield results. Spend five minutes with that first.
Jewelrers rouge, toothpaste, VIM(comet) work to.
The point being it is a simple polishing routine, get to it.
I used 400 grit sandpaper once, then 600, then 800, then 1200(for a long time), then rubbing compound then polishing compound then rouge.
No rocket science here, just polishing, Feel and hear the smoothness.
(It can be done with power tools, but you need to understand what polishing "IS" first, the area is so small it makes no sense to use power tools to do your headlights unless you are doing the car at the same time which means you understand what polishing is so "carry on").
Think of it this way, glaciers 'polish the earth', it's the same thing. You can't smooth a mountain with a rag but using the right grit you can clean a headlight if you choose the correct grit. Crystal clear is just one grit away from foggy.
Without the proper grit at the right time it is a big effort. I can get mirror result in minutes with the whole grit range and a bit of practise on ANY material. Everybodylikes shine so it is a good thing to learn. Imagine polishing you Ipod to mirror (laquaur) white, that is very easy to do.