A self-closing 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 tapered female connector orifice or by being forced open by a blunt cannula. The valve may be effectively used as a valving part in needleless connector adapters. A special method for constructing the valve when imposed upon by restrictive tolerances of a luer fitting is also disclosed. Examples of uses of the self-closing valve in male luer needleless connector adapters and closed mixing systems and closed mixing systems with flush are also disclosed. An application providing a closed male luer adapter, a closed valved male luer replacement for a syringe is disclosed as well as applications associated with closed system mixing syringes.