Just fought a similar battle with some water spots from a sprinkler.
Couple of links to some really specific articles on the subject:
http://www.autogeekonline.net/forum/...-type-iii.html
http://www.autogeekonline.net/forum/...ter-spots.html
http://www.autogeekonline.net/forum/...pots-hand.html
It took me 3 attempts, each time going more aggressive with the polish/compound, to get rid of them. Luckily I had a DA polisher. I don't think it could be done by hand.
Good luck!