A transmission with variable mechanical prestress including a pinion driven by an electric motor, a driven gearwheel with its bearings in a housing, and an electromagnetic actuator for applying a prestress force which is controllable in dependence on an instantaneous load to be handled by the transmission. The electric motor with the pinion is supported so that it can be tilted relative to the housing. Owing to a tilting movement of the electric motor caused by the actuator, the pinion is pressed against the gearwheel with a certain prestress force in a radial direction. The transmission is free from play, while the virtual play arising from friction and hysteresis is strongly reduced, and the positioning accuracy is enhanced as a result.