A valve has a major valve closure member with a valve stem for opening and closing a major port in a valve chamber. An alternate flow path extends through the major valve closing member. Flow is controlled through the alternate flow path by directing a minor valve actuating fluid through the valve stem to apply pressure on a minor valve piston in the major valve closure member to move a minor valve closure member in the major valve closure member between a closed mode in which the minor valve closure member closes the alternate flow path and an opened mode in which the minor valve closure member opens the alternate flow path. The minor valve actuating fluid is sealed from the alternate flow path by a flexible diaphragm positioned between the minor valve actuating fluid and the minor valve piston, so the pressure of the minor valve actuating fluid is applied to the minor valve piston via the flexible diaphragm.