  We study the Anderson orthogonality catastrophe (AOC) in finite conductors
with diffusive disorder. The disorder averaged logarithm of $\chi$, the overlap
between the ground states before and after adding a static impurity, is found
to depend nonmonotonically on the disorder. In two dimensions $<\ln\chi^{-1}>
\propto \ln^2 N$ in the weak disorder limit, thus showing a stronger dependence
on the number of electrons $N$ than in the canonical AOC. A very broad tail of
the distribution of $\chi$, found numerically, is a signature of the importance
of a few-level statistics at the Fermi energy.
