A method for controlling a quantity of medium transferable from a screen roller of a printing machine onto a roller that is in contact with the screen roller includes exerting an influence upon a difference in circumferential speed between the screen roller and the roller in contact therewith, and further includes controlling the difference in the circumferential speed as a function of the printing speed of the printing machine, so that printed medium density remains at least approximately constant at least within a wide printing speed range.