  We consider a superconductor-insulator-superconductor (SIS) junction in which
the tunnelling through the insulating barrier is dominated by a localized
``negative U'' center. We show that the $I_{c}R$ product of the junction
depends sensitively on the spectrum of impurity states, and in near resonant
condiditions exhibits an anomalously large I$_c$R product which can exceed the
famous Ambegoakar-Baratoff limit by an arbitrarily large factor. The analysis
is extended to problems in which there is an array of negative U centers in the
junction. We also discuss general reasons to expect significant violations of
the optical conductivity sum rule in most SIS junctions and of the
Ambegoakar-Baratoff result when the superconductors emerge from a non-Fermi
liquid normal state.
