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

Wegner estimate and localization for alloy-type models with sign-changing exponentially decaying single-site potentials