An apparatus for filling containers with a product includes a filling element, a supply line that supplies the product, a switching valve, a control valve, a vessel that is disposed between the switching valve and the control valve, and a volumeter that is disposed between the switching valve and the control valve. The vessel supplies a pre-metered quantity of the product for discharge via the switching valve to the filling element, the quantity having been pre-metered by the volumeter. The supply line provides the product to the vessel at a first flow rate. Discharge of the product through the switching valve and into the filling element occurs at a second flow rate that exceeds the first flow rate, the first and second flow rates being volumetric flow rates.