The presence of nonmagnetic impurities in a 2D ``bad metal'' depresses the
superconducting Berezinskii-Kosterlitz-Thouless transition temperature, while
leaving the pairing energy scale unchanged. Thus the region of the pseudogap
non-superconducting phase, where the modulus of the order parameter is non-zero
but its phase is random, and which opens at the pairing temperature is
substantially bigger than for the clean system. This supports the premise that
fluctuations in the phase of the order parameter can in principle describe the
pseudogap phenomena in high-Tc materials over a rather wide range of
temperatures and carrier densities. The temperature dependence of the bare
superfluid density is also discussed.Comment: 11 pages, LaTeX, 1 EPS figure; final version to appear in
Low.Temp.Phy