According to the invention, the rotational speed of the drum (42) of an ore mill (41) is controlled variably over time. By rotating the drum during a first time interval at high speed, especially hard or dense particles are broken up by tumbling. At the same time, during the first time interval the discharge characteristics of the mill are adversely affected. The first time interval is followed by a second time interval, in which the drum is rotated at a slower speed. In the second time interval the material is discharged more effectively, whereas the tumbling movement inside the mill cannot be achieved. The combination of said different modes of operation within short time periods in continuous operation improves on average both the comminution as a result of a tumbling motion of the material and also the discharge of the ground material. By regulating the rotational speed with different target values within short time windows, different requirements for the movement behaviour of the material to be ground and for the discharge characteristics of the ground material can be simultaneously optimised. This has the advantage that a higher throughput can be achieved for the mill.