At critical current density of the order of 100 kA/cm(2), tunnel Josephson junctions become overdamped and may be used in RSFQ circuits without external shunting, dramatically increasing circuit density. However, the physics of electron transport in such high-j(c) junctions differs from the usual direct tunneling and until recently remained unclear. We have found that the observed de I-V curves of niobium-trilayer junctions with j(c) = 210 kA/cm(2) can be explained quantitatively by resonant tunneling through strongly disordered barriers. According to this interpretation, random spread of critical current in high-j(c) junctions may be rather small (below 1% r.m.s.) even in deep-submicron junctions, making VLSI RSFQ circuits, with density above 10 MJJ/cm(2), feasible.