  We study the tails of the density of states (DOS) in a diffusive
superconductor-normal metal-superconductor (SNS) junction below the Thouless
gap. We show that long-wave fluctuations of the concentration of impurities in
the normal layer lead to the formation of subgap quasiparticle states, and
calculate the associated subgap DOS in all effective dimensionalities. We
compare the resulting tails with those arising from mesoscopic gap
fluctuations, and determine the dimensionless parameters controlling which
contribution dominates the subgap DOS. We observe that the two contributions
are formally related to each other by a dimensional reduction.
