I just realized that my United Airlines credit card from Chase uses the double-cycle billing method, one of the schemes currently under scrutiny by Congress. I had wondered about this earlier in the year, whenI started using this card as a "pay off every month" card for everyday purchases.  It seemed to take a number of months before I was no longer free of interest fees.  I found this clause in the "Grace Period" section of my cardholder agreement:

...we do not charge periodic finance charges on new purchases billed during a billing cylce if we receive both payment of your new Balance on your current statement by the date and time your payment is due and also payment of your New Balance on your previous statement by the date and time your payment was due.

I've added the italics for emphasis.  In other words, I will be charged fees on this month's bill, if I hadn't fully paid off last month's statement balance.  The practical effect is that it is difficult to get to a "no fee" state. You have to pay your full statement balance for 2 months in a row before you can use the card free of fees.  Unfortunately, the only way to determine if your card uses this scheme is to read the fine print in the cardholder's agreement.  As I did, look carefully in the "Grace Period" section for a statement similar to what I've shown above.

Should you stop using a card if you discover this scheme?  I don't necessarily recommend stopping use, but you need to be very careful with such a card.  For my United card, which I like because I build mileage points with United Airlines, I am doubly focused on never carrying over a balance.  Knowing the penalty of the double-cycle billing scheme actually serves as motivation to continue paying the balance in full.