Abstract: A metal or glass wire is etched with great precision into a very narrowly tapering cone which has the shape of the desired final capillary-optics bore. By controlling the rate of removal of the wire from an etchant bath, a carefully controlled taper is produced. A sensor measures the diameter of the wire as it leaves the surface of the etchant. This signal is used for feedback control of the withdrawal speed. The etched wire undergoes a treatment to produce an extremely low surface-roughness. The etched and smoothed wire is coated with the material of choice for optimizing the reflectivity of the radiation being focused. This could be a vacuum evaporation, sputtering, CVD or aqueous chemical process. The coated wire is either electroplated, built up with electroless plating, or encapsulated in a polymer cylinder such as epoxy to increase the diameter of the wire for easier handling and greater robustness.