A dispensing system is provided for a container having an opening to the container interior. The dispensing system includes a closure with an elevator that is disposed within the container opening for movement between a fully elevated position and a fully lowered position while the elevator is restrained by the container from rotating. The elevator has a seat defining an inlet passage and has a thread. A rotatable housing is mounted on the container at the opening and has a thread engaged with the elevator thread. The housing has a dispensing passage and an occlusion member. The occlusion member sealingly engages the elevator seat and prevents flow through the elevator inlet passage when the elevator is in the fully elevated position. When the elevator is moved away from the fully elevated position by rotation of the housing, flow is permitted through the inlet passage and into the housing dispensing passage. A flexible dispensing valve is sealingly secured across the dispensing passage in the housing. The valve has a self-sealing slit which opens to permit flow therethrough in response to increased pressure on the side of the valve facing the interior of the container.