Abstract: A closure for dispensing pills, capsules and the like includes a one-way valve member with a valved passage for opening to permit dispensing from the container when the container is in an active dispensing orientation, and for closing to prevent access to the interior of the container when the container is in an inactive non-dispensing orientation. A rotary system includes an upper cap member and a bottom member bridging the valve member, and the upper cap member has an egress passage located above the valved passage in the one-way valve member. The bottom member is keyed to rotate as a single unit with the upper cap member and includes a laterally projecting section aligned with the egress passage in the upper cap member for overlying the bottom of the valved passage in the one-way valve member when the egress passage of the upper cap member is aligned with the valved passage.