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I just did one of my cars. Had many swirl marks and mild scratches (not through the clear coat). First I washed and dried the car. I used a variable speed orbital buffer and foam polishing pad with a Meguier's product. The bottle stated 'for use to remove mild scratches prior to polishing and waxing'. There are many products on the market that will removed the scratches and swirl marks. Some areas required a second go around but, the car looks great now. Once satisfied with the results I hand waxed.
Any Mothers or Meguiars products will work fine as long as you have good towels. For fine scratches, I just hand polish, unless it's bad. I have a 5 1/2" pnuematic buffer that is great for tight areas and peaks of the fenders, and I have a big bulky automotive buffer, but only break that thing out for heavy duty jobs.