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We describe the fabrication and properties of high critical current density (J/sub c/) Nb/AlO/sub x//Nb Josephson junctions with deep-submicron dimensions. The junctions are fabricated using a planarized process in which all levels are patterned using a combination of optical and electron-beam lithography. The base and counter electrodes are defined by reactive ion etching using quartz etch masks to give a minimum feature size of 0.2 microns. For J/sub c/=2.1 mA//spl mu/m/sup 2/ and junction area less than 0.1 /spl mu/m/sup 2/ the devices are self-shunted and exhibit nonhysteretic I-V characteristics. A small hysteresis in the larger junctions is caused by heating in the electrodes.