A milking device and method for removing a teat cup from a teat of an animal are disclosed. The teat cup has a teat space for containing a teat and is connected via a milk tube to a vacuum source for generating a milking vacuum. A drawing-away device is provided for drawing the teat cup away from the animal only after a vacuum-lowering device has lowered the milking vacuum in the teat space below a threshold value. The level of vacuum may be measured by means of a vacuum sensor.