We describe a process for fabricating submicron Josephson junctions suitable for integration in small and medium scale integrated circuits. This junction process utilizes a double layer SiO2 lift-off process in a cross-type geometry to define Josephson junctions. A photoresist strip with an arbitrary length and a fixed width defines the length of the junction. Its width is defined simultaneously with the metallization strip that crosses the first strip. The double layer SiO2 insures a pinhole-free oxide and yields excellent insulating properties suitable for medium scale circuit applications. We used this process to fabricate Nb/AlO(x)/Nb and NbN/MgO/NbN tunnel junctions as small as 0.5-mu-m2 with figures of merit (V(m)) larger than 30 mV. We report on the repeatability of this process and its utility in high current density Josephson junction circuits.