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For me at least, using a dual action orbital, both Meguiar's polishing and finishing pads and sometimes following up with a less aggressive product to remove any possible micro-marring, I have swirls (and minor scratches) before and they're gone after using Ultimate Compound.
Good product, does a good job; but remember Ultimate Compound is fairly aggressive and you may not need something that aggressive. A test area with less aggressive products is usually recommended. Plus performing proper hand washing and clay-barring before starting paint cleaning/correction is helpful.
And if you haven't at least read Todd's recent post, you should before beginning.