I've set the default payment method on the country. But after I finished an order, the new order has the same shipping method as the one I just finished.

This causes problems because some of my payment methods are free and some have a small cost. So the UI shows that the empty cart still has a cost, even though its empty, if I've finished an order with a payment mehtod that has a cost. (I've double checked that its not my code that displays the wrong numbers.)