A pump comprises a housing (141) having a cavity (142) with an inlet valve (143), an apparatus (144) for raising fluid pressure in the cavity (142) and a discharge valve (145), the discharge valve (145) comprises a valve head (160) movable between an open and closed position and a valve seat (167), wherein the pump further comprises a booster piston (182) arranged in a booster cylinder (183), the booster piston (182) has a first face (191) exposed to a low pressure zone (189) and a second face (194) exposed to fluid pressure in the cavity (142), and at least one of the booster piston (182) and the booster cylinder (183) is movable relative to the other to add an opening force to the discharge valve. The pump is preferably a mud pump for circulating drilling mud through a drill string in a wellbore or a cement pump which may be of the type for pumping cement into a wellbore. Also disclosed is a method for facilitating opening a valve comprising a valve head (160) and a valve seat (167), the valve head (160) is movable a predetermined distance from a closed position on the valve seat (167) to a fully open position distant on the valve seat, and the method comprises the step of adding a force to the valve head (160) along a small portion of the predetermined distance.