MX52Z

And a spray bottle full of water. This is not a five minute job. It took me a couple hours per headlight on a different car, each clamped to a workhorse with lots of wet sanding using increasingly higher grit pads and then finally a blue creme compound.

I got them as clear as possible but still slightly duller than factory new until I sprayed the final coat of seal (SEM SolarRay) and cured them with a UV light. Then they looked like new. If you just wax them as the final step, they'll haze again in a couple months.

Granted, I started off with milky white headlights, almost opaque. The OP's lights look pretty good to start with. I'd probably just wet compound them.