  We analyze the rectification properties of voltage-biased Josephson junctions
exhibiting the superconducting diode effect. Taking into account multiple
Andreev reflection (MAR) processes in our scattering theory, we consider a
short weak link of arbitrary transparency between two superconductors with
finite Cooper pair momentum $2q$. In equilibrium, the diode efficiency is
bounded from above in this model, with maximal efficiency $\eta_0\approx 0.4$.
Out of equilibrium, we find a rich subharmonic structure in the current-voltage
curve. For high transparency and low bias voltage $V$, the rectification
efficiency $\eta(V)$ approaches the ideal value $\eta=1$ for $q\xi\to 1$ (with
coherence length $\xi$).
