A pump comprises a housing having a fluid inlet and a fluid outlet. A piston is mounted for reciprocating motion in first and second directions within the housing. The housing has first and second cavities on first and second sides of the piston, respectively. The first and second cavities are fluidly coupled to the fluid inlet and fluid outlet, so that fluid is pumped to the fluid outlet when the piston moves in either of the first and second directions. A bleed valve is coupled between the first and second cavities. The bleed valve has first and second closed states and an open state. The bleed valve changes from the first closed state through the open state to the second closed state when the piston moves in the first direction. The bleed valve changes from the second closed state through the open state to the first closed state when the piston moves in the second direction.