The invention relates to a control device (100) for a brake system of a vehicle, by means of which control device (100) the brake system can be controlled in a first operating mode in which, in the case of activation of a brake activation element (64) applied by a driver, a buildup of brake pressure is prevented at least in a first wheel brake calliper (53a) of a first brake circuit (50) of the brake system, while during the first operating mode a first wheel inlet valve (74a) of the first wheel brake calliper (53a) can be placed at least temporarily in an at least partially open state, and a first wheel outlet valve (78a) of the first wheel brake calliper (53a) can be kept in an at least partially open state, wherein a second wheel inlet valve (75a) of a second wheel brake calliper (54a) of the first brake circuit (50) can be placed in an at least partially open state, and a second wheel outlet valve (79a) of the second wheel brake calliper (54a) can be placed in a closed state, in such a way that a brake pressure can be built up in the second wheel brake calliper (54a). Furthermore, the invention relates to a method for operating a brake system of a vehicle.