Being a Brazilian myself, I must say that our original recipe for Caipirinha takes lemon (Tahiti lemon), not lime.
One more hint: I know this could be hard for you to find in the USA, but try using the artesanal Cachaça, not the industrial one. If you have more than a few drinks, the industrial Cachaça (Velho Barreiro, Ypioca, 51) will probably give you a headache and a hangover the next day. A good quality Cachaça (artesanal), won't! Cheers from Brazil!!!