The rapid onset of quasiparitcle tunneling current in superconductor‐insulator‐superconductor (Josephson) junctions at voltages above 2&Dgr;/eis being used for millimeter‐wave heterodyne mixing. Junctions with a 2‐&mgr;m diameter andRN=50 &OHgr; have little capacitive shunting at the signal frequency of 36 GHz. Because there is no series resistance, residual capacitance can be tuned out. Double sideband conversion efficiencies of 0.32 and mixer noise temperatures as low asTM⩽7 K=4h&ngr;/khave been observed. The results are compared with shot‐noise‐limited mixer theory. Photon‐assisted tunneling effects are seen which indicate the approach to photon‐noise‐limited operation.