A simple two-layer channel model with a topographic barrier is used to study the response of the overflows across the Greenland-Scotland Ridge to changes in the available volume of deep and intermediate waters in the Nordic Seas. Hydraulic control determines the deep exchange through the different gaps in the ridge while a geostrophic balance in the north provides the respective upstream conditions. In the model the overflow through Denmark Strait is more sensitive to changes in the deep water supply than that of the Faeroe-Bank Channel, but no sudden breakdown of the exchanges across the ridge is seen when the supply decreases. Transport variations in the East-Greenland Current have only minor influence on the total overflow.