  We analyze the transport through a narrow ballistic superconductor-normal-
metal-superconductor Josephson contact with non-ideal transmission at the
superconductor-normal-metal interfaces, e.g., due to insulating layers,
effective mass steps, or band misfits (SIN interfaces). The electronic spectrum
in the normal wire is determined through the combination of Andreev- and normal
reflection at the SIN interfaces. Strong normal scattering at the SIN
interfaces introduces electron- and hole-like resonances in the normal region
which show up in the quasi-particle spectrum. These resonances have strong
implications for the critical supercurrent $I_c$ which we find to be determined
by the lowest quasi-particle level: tuning the potential $\mu_{x0}$ to the
points where electron- and hole-like resonances cross, we find sharp peaks in
$I_{\rm c}$, resulting in a transitor effect. We compare the performance of
this Resonant Josephson-Transistor (RJT) with that of a Superconducting Single
Electron Transistor (SSET).
