A self-closing twisted slit valve which is opened by compression inside a receiving tapered female orifice. For luer fittings, internal taper of a female luer fitting provides sufficient distortion of an asymmetrical valve to distort a closed, preferably planar slit to a patent fluid pathway. The slit may be opened by valve displacement into a female connector orifice or by being pierced by a blunt cannula. The valve may be effectively used for both needleless connectors and for needleless connector adapters.