We study the opening of transport channels in mesoscopic ballistic supercon
ductor-normal-metal superconductor Josephson contacts. Determininig the qua
siparticle excitation spectrum in the normal contact region as a function o
f gate voltage, we discuss the transformation of the electronic levels into
phase-sensitive Andreev levels with increasing chemical potential. The ope
ning of these superchannels leads to a supercurrent quantization that exhib
its nonuniversal behavior in general, and we discuss its dependence on the
junction parameters.