Jeff,
Swirls in your paint usually mean that a high speed buffer was used on the paint at some point. If this be the case then a high speed buffer can also remove them. In the hands of an expert that is.
One can also remove swirls by a safer method which is to use a random orbitol buffer, such as the Porter-Cable or the Cyclo dual head polisher. One can even remove swirls by hand with the proper technique.
I, as a detailer do not share all my "secrets", but I will give you a few tid bits. If the swirls are real bad then you may want to seek a highly recommended detailer in your area. If they are mild to just a few then rool up your sleeves and DIY.
If the paint is in fair to great condition, meaning it has no oxidation or contamination in it then proceed with these steps after washing the paint. Use Meguirs #3 if in great shape and #82 if in fair shape. Place the product on a sponge or foam applicator pad and rub one small portion out at a time in a bumper to bumper motion. Do not use circle motions. Wipe the surface down as you go, folding your wipe down towel often.
Use a new towel and applicator pad as build up gets on them. When you have rubbed out the entire painted areas, switch to Meguirs #9 and polish by machine, random orbitol if possible. Buff the paint "wet", meaning do not buff the product until it is dry tot he bone and evaporating. Think of #9 as a lotion to lubricate the paint. When you have done, say the front fender, take a clean foam pad and apply more #9 by hand, once again going back and forth, bumper to bumper.
Wipe down using, if at all possible a Micro-fiber towel or a flannel cloth. Use these because they are lint free and less likely to scratch. Top off with Meguirs # 26 or Pinnacle and it should look great. This is not a one or two hour job so plan to spend at least one day just rubbing it out. It's a labor of love and remember, in the world of detailing, "less is more"
Anthony
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"For A Beautiful Appearance You Must First Preserve" - Anthony Orosco