A pump for a high-pressure cleaning appliance for delivering cleaning liquid is provided. The pump has a pump housing with at least one pump chamber into which at least one piston plunges. The pump chamber is connected via at least one inlet valve to a suction line and via at least one outlet valve to a pressure line. A bypass line leads from the pressure line to the suction line. An overflow valve is arranged in the bypass line. The valve body of the overflow valve is connected to a control element which, in dependence upon the flow rate of the cleaning liquid, displaces the valve body to a closed or an open position. A rear housing component and a front housing component of the pump housing are joined together. The bypass line opens into a suction line section of the suction line, which extends between the housing components.