Piling on the credit cards

I just applied for my 3rd credit card in 12 months. 

This is not as crazy as it sounds.  I received, conservatively, an equivalent to $1750 in frequent flyer miles for opening these cards.  The cards are from United, American Airlines, and Continental, the last of which is still available.

Since the first year’s annual fee is waived, I keep the cards for 11 months and then cancel before hitting the first anniversary.  I use them for a few months and always pay off the full balance.  The way I see it, as long as I continue to use a very small portion of my available credit, closing a card won’t have an adverse impact on my credit rating. Somebody please tell me if I’m wrong and quietly burning in credit hell.