Banks are starting to charge fees to their best customers in response to a slew of new credit card industry regulations that will limit when they can raise interest rates, WCBSTV reports.

Bank of America already begun notifying its customers who pay their credit card bills in full every month that they will be charged a new annual fee of $29 to $99, and Citigroup is ramping up to follow suit.

"They can either pay that fee or they can close the account, and if they have had the account for a while and they close it, they are potentially going to hurt their credit card score," says Ben Woolsey, Director of Consumer Research at CreditCards.com.

"There is a big segment of their population that they will have never made money on, which is people who pay their bills on time every month," Woolsey notes.

Analysts say right now the banks are trying to figure out what their customers will tolerate.

Bloomberg reports that none of the credit cards offered online by the 12 largest U.S. banks would meet requirements of new federal curbs on the industry’s rates and fees, according to a report from the Pew Charitable Trusts.

The study, which examined almost 400 cards advertised by banks and credit unions and compared terms for cards offered in July 2009 and December 2008, found that all the cards surveyed used practices considered “unfair or deceptive” by the Federal Reserve.