For the least secure retailer I ever tested for you need:
The Credit Card Number
Security Code
Card Owner Name
Billing Address
And Phone number.

Whoever you purchase from will likely maintain a fraud list. They usually keep a blacklist of names, shipping addresses, known stolen credit cards (stolen cards that have been tried at that site), e-mail addresses.

After getting past them, you have to get past the merchant account. They know what cards were reported stolen, and flags get set off for unusual activity.

If you get caught, they will most likely start looking at the shipping address. I can't really think of a way around it, other than a P.O. box, or temporary address you can bail on. I've heard of people setting up bogus establishments at rented spots, or tricking people into receiving and forwarding goods.

Your safest bet is to try to milk as many cash advances as you can instead of online purchases. You can also try in store purchases if you know the cashier, but I wouldn't recommend doing it more than once.