The invention relates to a one-way valve, a device having the one-way valve, and a method for manufacturing the device. On one aspect, the one-way valve comprises a valve seat defining a first middle portion and first marginal portions; and a flexible valve cover which is superimposed on the valve seat and defines a second middle portion and second marginal portions. The flexible valve cover and valve seat form a valve seam therebetween. The valve seam defines an inlet and an outlet axially spaced relative to the inlet. The valve cover and valve seat define a first degree of interference therebetween at the inlet, and a second degree of interference therebetween at the outlet that is less than the first degree of interference. The valve cover is movable in response to fluid at the inlet exceeding a valve opening pressure between (i) a normally closed position with the first and second mid-portions in contact with each other and defining the normally closed seam, and (ii) a second position with at least a portion of the valve cover spaced away from the valve seat to allow the fluid to pass through the seam from the inlet through the outlet.