If they have a good covering of fat, brining will do little good.  On fully cooked hams, I make about six slits in the fat and stick a clove of garlic in each one (make sure to take them out when the ham is cooked).  Double wrap the ham in aluminum foil and before closing up cover with brown sugar and either peach preserves or apricot preserves.  Put in the oven at 180 degrees when you go to bed.  Take it out the next morning and let it set wrapped up.  Ready to eat for lunch.  All you're really doing is bringing it up to temperature very slowly.