Abstract: A pneumatic calibration system and the pump therefore, the system comprising a first fluid containing chamber for attachment to a device to be tested, a valve coupled to the first chamber to remove the fluid from the first chamber and a pump structure for providing a predetermined pressure to the fluid in the first chamber. The pump comprises a first piston disposed and moveable within first chamber to vary the volume of first chamber, a second piston, a second fluid containing chamber communicating between the first piston and the second piston, the second piston providing a predetermined pressure to the fluid in the second chamber and an expanding sleeve valve communicating between the first chamber and the second chamber to minimize the pressure differential across the first piston. The position of the first piston is adjustable in the first chamber. The second chamber includes a first portion and a second portion with a sleeve valve disposed therebetween.