The present invention relates to a milking device for milking a dairy animal, including at least one teat cup including a flexible cup liner around a teat space, and a single pulsation space and a milk line, a milking vacuum pump connected to the milk line, for providing a milking vacuum, a pulsator connected to the pulsation space, for providing a controllable air pressure therein, and a control device for controlling at least the pulsator during at least a milking action. The control device is configured to cause the pulsator and/or the milking vacuum pump to provide, in a period of time consecutive to a milking action wherein a dairy animal is milked and a teat is located in the teat space, such a substantially stable, non-pulsating pressure difference between the pulsation space and the teat space, that the cup liner shuts off the teat space from the milk line.
