The embodied mobile cranes have a travelling base structure that allows for travel of the crane over a surface. The cranes have a revolving superstructure mounted on the base structure and a boom and a backmast. The boom and backmast are each hinged about an associated pivot axis to horizontal the superstructure. The crane has a main load hoisting manner associated with the boom for hoisting a load. A superstructure ballast is supported on the superstructure. The cranes have a superlift ballast and associated connection manners to connect the superlift ballast to the backmast while the superlift ballast is resting on the surface and/or suspended from the backmast above the surface. The travelling base structure is provided with superlift ballast support to support the superlift ballast on the base structure so that the superlift ballast is movable along with the mobile crane while being supported by the base structure.