A precompression system for a liquid dispensing device is presented, that prevents liquid from being discharged until a predetermined pressure has been built up. The system comprises a pump for drawing liquid through an inlet and discharging it through an outlet, and a precompression valve disposed between the pump and the outlet. The valve allows liquid in the pump to reach the outlet once the predetermined pressure is established, and stops liquid from reaching the outlet once the pressure falls below it. The precompression valve comprises an elastic diaphragm normally closing the valve opening, with a concave surface facing the valve opening and in fluid communication with the pump and a convex surface in fluid communication with atmospheric pressure. The diaphragm may be stretched around a valve seat. Methods of assembling such a precompression system in a dispensing device are also presented.