An improved method and apparatus is provided to control the moisture content of pulp which is discharged from a press. During operation of the press, slurry containing the pulp enters the press and engages a screw which is rotated to feed the pulp upwardly in the press. As the wet pulp moves upwardly, water is removed from the pulp. In order to further reduce the moisture content of the pulp, a restrictor member or cone in the press outlet is effective to compress the pulp against helical flighting of the screw. In order to maintain the moisture content of the discharged pulp substantially constant with variations in wet pulp consistency and to prevent overloading of the press drive motor, the restrictor cone is movable axially along the screw drive shaft to vary the extent to which it restricts the press outlet. The restrictor cone is moved along the screw drive shaft under the influence of forces applied against the outer surface of the cone by the wet pulp. This movement of the cone adjusts the extent to which the outlet from the press is restricted and the extent to which the wet pulp is compressed with variations in the consistency of the wet pulp.