A300-B4 freighter has a minimum zero fuel mass of 191800lbs although the empty mass is about 181000lbs. So if we have no payload we carry about 11000lbs of ballast fuel.
I was told that this minimum mass was the lowest that was tested for in the development of this aircraft, as with pax equipment it would never be less than 191800lbs. So this is a certification limitation.
Airbus did not plan for a freighter version at the start.
The only time this has been a problem was when trying to fly from Sharja to Stansted direct with no load and full tanks required. The ramp guy could not understand why we could not go direct unless he could find us some freight or ballast. I think we loaded a lot of empty pallets to solve the problem.
Hope this helps.