No, thrasher, they don't do that. For balances at the same interest tier, they apply payments to the oldest charges first.
So if you are carrying a balance from one month to the next, as long as you pay the amount from one statement by the due date on that statement, you won't incur any finance charges. They won't apply that payment to any new charges that haven't appeared on a statement until prior statement balances are paid off.
They don't do that because the T&C say you have a grace period on new charges. They have to honor that.
Is that what you're getting at?