A flexible, resilient, self-sealing slit-type valve (40, 140, 240, 340) is provided with a configuration that minimizes the difference between the pressure differential at which the valve opens and the pressure differential at which the valve (40, 140, 240, 340) closes. The valve (40, 140, 240, 340) includes a peripheral mounting portion (42) and a valve head (60, 160, 260, 360) connected thereto. The valve head (60, 160, 260, 360) has an interior surface (78, 178, 278, 378) and an exterior surface (76) which each has a recessed configuration such that the thickness between the exterior surface (76) and interior surface (78, 178, 278, 378) is thinner at the center on the longitudinal axis (62) of the valve (40, 140, 240, 340) than at a radially outward location.