HOLOGRAMS.....not swirls. If there are swirl marks, the washing induced circular marring, then it will be easy to polish out. Holograms will need compounding to remove if deep enough.
Have someone do a solid two step on the car....something like megs 83, then megs 80 should do the trick no problem.
menzerna IP/FPII will too, and a number of other combos, but you are going to have to remove the holograms, and the swirl marks if there are any will go with it!
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