  We analyze nonperturbatively the behavior of a Josephson junction in which
two BCS superconductors are coupled through an Anderson impurity. We recover
earlier perturbative results which found that a $\delta=\pi$ phase difference
is preferred when the impurity is singly occupied and the on-site Coulomb
interaction is large. We find a novel intermediate phase in which one of
$\delta=0$ and $\delta=\pi$ is stable while the other is metastable, with the
energy $E(\delta)$ having a kink somewhere in between. As a consequence of the
kink, the $I-V$ characteristics of the junction are modified at low voltages.
