A dispenser comprising a body defining a variable-volume storage chamber and a dispensing portion defining a bore coupled in fluid communication with the storage chamber, an outlet aperture coupled in fluid communication with the bore, and a one-way valve. The valve includes an axially-extending valve seat and flexible valve cover seated on the valve seat, defining a normally-closed, axially-extending seam therebetween forming a fluid-tight seal. The valve cover is movable relative to the valve seat and the seam is connectable in fluid communication with the outlet aperture. The dispenser further comprises an actuator and piston assembly including a piston receivable within the bore, a manually-engageable actuator connected to the piston for moving the piston between first and second positions relative to the bore to dispense substance within the bore through the outlet aperture and out of the dispenser.