Dispenser valves include a valve outlet, which has a closure element configured to assume an opened condition when the pressure differential across the dispenser valve reaches a cracking pressure. The dispenser valve configured to flow in one direction when the closure element is in opened condition. A pump mechanism is configured to pump dispensable product from the connection to the dispenser valve. It generates the cracking pressure needed to configure the closure element in the opened condition. It is provided as a duckbill valve and a reed valve.