A dispenser has a body defining with a variable-volume storage chamber for storing product. A compression chamber is in fluid communication with the storage chamber for receiving substance therefrom A one-way valve of the dispenser includes valve seat and flexible valve cover seated on the valve seat and defining a normally-closed seam therebetween forming a fluid-tight seal between the valve cover and valve seat. The flexible valve cover is movable relative to the valve seat to allow the passage of substance through the seam and out of the dispenser. A manually-engageable actuator connected to the dispensing portion is movable between first and second positions to dispense substance within the compression chamber out of the dispenser.