A dispenser for dispensing a substance, such as a pharmaceutical, ophthalmic, dermatological, cosmeceutical, cosmetic or other product, has a body with a variable-volume storage chamber for storing the product. A dispensing portion of the dispenser is connected with the body and has a compression chamber in fluid communication with the storage chamber for receiving substance therefrom, and an outlet aperture coupled in fluid communication with the compression chamber. 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 a manually-engageable actuator connected to the dispensing portion movable between first and second positions to dispense substance within the compression chamber through the outlet aperture, and an integral, dome-shaped spring for biasing the actuator in a direction from one of the first and second positions toward the other.