The digester and method are for the continuous cooking of pulp. At least two withdrawal positions (11E, 11D) for cooking fluid are arranged at different heights in the digester (10). The cooking fluid in the first and second position is withdrawn after the chips have had a retention time that differs by at least 10 minutes. The differential pressure between the positions is determined and when this exceeds a pre-determined level, a connection (17E) opens between these positions, establishing a flow parallel to a flow of cooking fluid between these positions in the digester. Several withdrawal positions are preferably connected in a common shunt system (17A-17F), with valves (18A-18F), controlled by the differential pressure, that are located between adjacent positions.