The invention relates to a dispenser, particularly suitable for a liquid container, comprising: an air pump with an air cylinder (23) and an air piston (3) axially displaceable in the air cylinder, an air space (19) defined between the air cylinder and the air piston, supply-closing means (39) for closing the air supply to the air pump, discharge-closing means for closing the air discharge from the air pump, a cover (1) connected to the air piston, an air inlet opening (12) in the cover, wherein the air inlet opening debouches directly into the air space, and an annular element (39) which extends axially on the inside of the cover and which comprises an edge part, which edge part is in contact with at least the part of the inner wall of the cover located around the air inlet opening (12).