We prove pure point spectrum with exponentially decaying eigenfunctions at all band edges for Schrödinger Operators with a periodic potential plus a random potential of the form Vω(cursive Greek chi) = ∑qi(ω)f(cursive Greek chi - i), where f decays at infinity like |cursive Greek chi|-m for m > 4d resp. m > 3d depending on the regularity of f. The random variables qi are supposed to be independent and identically distributed. We assume that their distribution has a bounded density of compact support.