Disclosed in this specification is a hand-operated dispensing pump for dispensing viscous fluids. The container includes a flexible cap attached to the bottom portion of the container that defines a fluid pumping zone. An elongated tube extends from this zone to a spout that is disposed atop the container. The cap is equipped with at least two one-way valves that selectively permit fluid to pass into the pumping zone when the cap flexes in a first direction and permits fluid to pass out of the pumping zone and out the spout when the cap flexes in a second direction.