A dispenser for dispensing a substance, such as a pharmaceutical, ophthalmic, dermatological, cosmeceutical, cosmetic or other product, has a body defining a variable-volume storage chamber for storing the product. A dispensing portion of the dispenser is connected with the body and defines a bore coupled in fluid communication with the storage chamber for receiving substance therefrom, and an outlet aperture coupled in fluid communication with the bore. A one-way valve of the dispenser includes an axially-extending valve seat and an axially-extending flexible valve cover seated on the valve seat and defining a normally-closed, axially-extending 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 and the seam is connectable in fluid communication with the outlet aperture to allow the passage of substance through the seam and out of the dispenser. 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 an integral, dome-shaped spring coupled to at least one of the piston and the actuator for biasing the piston in a direction from one of the first and second positions toward the other.