I'm trying to imagine a situation where a credit card company would NOT want even just the revenue from transactions, and I can't really imagine it. Unless you charge very, very little, carry no balance, always pay on time, and tie up a customer service person on the phone several times a month, it's hard for me to imagine that the CC company wouldn't want your business.

Actually, I've also heard the opposite situation--that customers with large balances are offered incentives to pay them off sooner rather than later. Apparently, the logic behind that is that all these large CC balances appear as liabilities on their balance sheets. One way to look stronger financially is to push down the liabilities on your books.