A parking brake having an actuator, wherein the actuator is driven by a direct current motor which can be operated in two directions. The actuator moves, via a self-locking gear mechanism of the actuator, at least one brake shoe for applying or releasing the parking brake in the direction of a rotary element or away therefrom. A control unit for performing open-loop or closed-loop control of the movement of the direct current motor is also provided. The parking brake is designed such that, when the parking brake is applied or released, an application point of the brake shoes against the rotary element is generally overshot. In order to increase the accuracy and reliability of the setting of the brake-application force when the parking brake is applied or of the brake-application clearance when the parking brake is released, the control unit determines the application point by forming the first derivative over time of the electric current taken up by the direct current motor during the application of the brake. A corresponding method for operating such a parking brake is also described.