A foam-dispensing pump includes an actuator, a collar, a housing, an air piston, a liquid piston, a mesh element and an air valve structure. The collar is constructed and arranged for attachment to a liquid storage container and a portion of the actuator is received by the collar. The air piston is constructed and arranged to be moveable within the housing. The liquid piston is constructed and arranged to be moveable within the housing. The mesh element is constructed and arranged to receive air and liquid for the production of foam. The air valve structure includes an annular sleeve component which is assembled onto the liquid piston and a cooperating annular valve element which is received by the air piston.