I've never had the problem, but like T, I tend to either crack the lid or leave it off to burn off the leftover charcoal. I guess I've never tried to save the charcoal figuring it was pretty much spent and would not behave the same way as fresh for the next cook. Also makes clean up a lot easier.
I do try to cook as much as I can each time to maximize the value of the full basket of charcoal. So, generally there is not a lot left.
I have to wonder if when closing everything down to smother the fire, if this doesn't create a different type of smoke as the coals die...