A control device is described for a brake system of a vehicle, having a valve control device that is designed to determine, at least taking into account a provided information signal relating to a generator braking moment of a generator that is currently being exerted or is to be exerted, a first target state of a first valve of the brake system that is connected to a master brake cylinder of the brake system and to a fluid storage device of the brake system in such a way that a brake fluid volume can be displaced out of the master brake cylinder into the fluid storage device via the first valve, which is controlled into an at least partly open state, and to output a first control signal, corresponding to the first target state, to the first valve, the first target state being determinable, by the valve control device, for a valve connected via at least one intake line to a brake medium reservoir of the brake system as fluid storage device, as first valve. In addition, a method is described for operating a brake system of a vehicle.