Removing swirl marks, fine scratches from chrome?

[DanMcG]

I've got a used bumper, maybe aftermarket, that is real nice, until you get close to it then you see a lot of swirl marks. Any tips or tricks to remove them?

Here's what I'm talking about. The spots you see are dust and not pitting.

 

[Chris_Hamilton]

Not saying this is the correct way or only way but it works fairly well provided the scratches aren't excessive.
Get some 4aught (0000) steel wool. Use a polish or compound like what is used to buff paint with. I normally use polishing compound first, if that isn't aggressive enough then I'll try the more aggresive compound. The 3D compounds we use for paint buffing work really well for this ADA500 and ADA520. Then add some polish on the surface and some on the steel wool. Start rubbing in tight circles. Use a little water in a spray bottle to keep things wet. Continue rubbing in tight circles till you have gone over a section twice. Then use micro fiber towel and clean up the surface. Nearly all the scratches should be gone.

You could also use a traditional buffing wheel (not paint correction type buff) and some ultrafine (rouge?) polish. I found that to be more labor intensive or rather harder to do correctly, and you need to have the right wheel and polish for it to work. Not to mention the correct tool and buff holder.