  We study Schr\"odinger operators on $L^2 (\RR^d)$ and $\ell^2(\ZZ^d)$ with a
random potential of alloy-type. The single-site potential is assumed to be
exponentially decaying but not necessarily of fixed sign. In the continuum
setting we require a generalized step-function shape. Wegner estimates are
bounds on the average number of eigenvalues in an energy interval of finite box
restrictions of these types of operators. In the described situation a Wegner
estimate which is polynomial in the volume of the box and linear in the size of
the energy interval holds. We apply the established Wegner estimate as an
ingredient for a localization proof via multiscale analysis.
