A pump includes a pump body having an admission valve movable therein to alternately block and unblock a valve seat to connect a low pressure space to a pumping chamber. A control valve is positioned fluidly between a control chamber and the low pressure space, and moves between a closed position where the control chamber receives high pressure for hydraulically actuating the admission valve, and an open position where the control chamber is connected to the low pressure space to enable closing of the admission valve. The pilot actuation of the admission valve produces a greater travel distance and efficiency than what might be available with certain other actuating mechanisms.