A bellows-type pump includes a body portion with an inlet and an outlet. A bellows member is secured to the body portion and provides a dosage volume that communicates with both the inlet and outlet. Compressing the bellows member causes a sealing web thereof to contact the inlet and seal the same against the flow of product from within the dosage volume. The sealing web does not cover the outlet upon compression of the bellows member and, thus, product is dispensed through the outlet upon such compression. Expansion of the bellows member draws product in through the inlet.