A brake system, and a method for operating a brake system of a vehicle. To reduce a braking force, brake fluid is able to be discharged from the braking device via a cross-section adjusting member which connects a delivery device to the braking device, in a controlled and/or regulated manner, into an intermediate reservoir and is delivered to the main brake cylinder using the delivery device. The discharge of the brake fluid from the braking device of the brake system takes place, at least at times, at a discharge volume flow that is greater than the maximum delivery volume flow of the delivery device, and when a certain operating state of the braking system occurs, the discharge volume flow is reduced.