In order to be useful for high speed digital circuit applications, double-barrier SINIS or SIS'IS junctions must be nonhysteretic, possess high critical current densities (j/sub c/>1 kA/cm/sup 2/) and high characteristic voltages V/sub c//spl sim/0.3 mV, where V/sub c/=I/sub c/R/sub sub/ and R/sub sub/ is a characteristic (subgap) resistance damping the junction in the operating range of voltages. This requires high transparencies of barriers and small interlayer thicknesses. Data are presented on fabrication and Josephson properties of SIS'IS junctions with j/sub c/ up to 10 kA/cm/sup 2/ at 4.2 K. It is shown that the asymmetry of double-barrier structure starts playing a major role at high j/sub c/ (i.e., at thin, high transparency barriers) as evidenced by the temperature dependences of the critical current, the value of the current deficit in the I-V characteristics, and the appearance of multiple Andreev reflection peaks in differential conductance of the junctions.