The present invention makes an improved braking system available. This comprises a brake pedal and/or a servo unit and also incorporates a hydraulic unit including an integrated electronic controller (for short: EBS) and a hydraulically actuated wheel brake associated with each wheel. Hereby, the wheel brakes are connected hydraulically to the electronic hydraulic unit as is also the brake pedal/servo unit. A brake cylinder for the wheel brake is arranged to be prefilled by means of a “prefill” function in order to at least partly reduce the clearance gap. For the first time hereby, the braking system is provided with a switching device by means of which the “prefill” function is arranged to be switched on or off in dependence on a selectable operating mode. Moreover, the invention proposes a method for electronically regulating the brakes utilizing such a braking system.