Convertible top assembly for a vehicle with a passenger compartment, comprising a convertible top which can move between a closed position, in which the convertible top covers the passenger compartment of the vehicle, and an open position, in which the passenger compartment is open, and a hydraulic actuating device for moving one or more components of the convertible top assembly, the actuating device comprising a hydraulic pump with an associated drive motor and a reservoir for hydraulic fluid, as well as one or more hydraulic actuators, the actuators acting on the convertible top assembly and the pump being designed to supply pressurized hydraulic fluid to the actuators. The actuating device comprises control means which are designed to regulate the volumetric output of the pump while the convertible top assembly is being actuated.