A tensioning device for a continuous drive element includes a housing, a tensioning piston movably guided in the housing, and a pressure chamber for hydraulic fluid formed between the housing and the tensioning piston, wherein the tensioning piston comprises a vent opening, and a vent channel between the pressure chamber and the vent opening, formed by assembling at least two vent elements, wherein in the one vent element, in the contact surface to the second vent element, separate partial areas of the vent channel are formed by molded groove sections which are connected to each other by transfer grooves molded in the second vent element in the contact surface to the first vent element, such that sections of a main portion of the cross-section of flow of the vent channel are arranged on one side, and sections are arranged on another side of a plane spanned by the contact surfaces.