A method and device for driving an arrangement, in a vehicle, that delivers a pressurized medium in a brake system, the pressurized medium being delivered in at least one brake circuit of the brake system, and a pressurized medium volume available in the brake circuit being dependent upon the driving of the arrangement delivering the pressurized medium. In this context, the arrangement delivering the pressurized medium is driven as a function of the vehicle speed so as to effect a correlation between the vehicle speed and the pressurized medium volume available in the brake circuit. This means, in particular, that the vehicle speed and the pressurized medium volume available in the brake circuit are linked in such a way that, with rising vehicle speed, the available volume of pressurized medium in the brake circuit is increased, and/or with falling vehicle speed, the available volume of pressurized medium in the brake circuit is decreased. This ensures that a sufficient volume of pressurized medium is available, even in the case of heavy volumetric consumption during a brake application, in which the arrangement delivering the pressurized medium does not adequately supply the pressurized medium.