A control device for a brake system of a vehicle includes a valve control device, using which, while taking into account a provided information signal with respect to a currently exerted or to be exerted generator braking torque of a generator, at least one high-pressure switching valve of a brake circuit of the brake system is able to be controlled into an at least partially opened state such that a brake fluid volume is able to be displaced from a main brake cylinder of the brake system into a storage chamber of the brake circuit via the at least one high-pressure switching valve that has been controlled into the at least partially opened state. Furthermore, a method for operating a brake system of a vehicle is described.