  We use scattering theoretic methods to prove strong dynamical and exponential
localization for one dimensional, continuum, Anderson-type models with singular
distributions; in particular the case of a Bernoulli distribution is covered.
The operators we consider model alloys composed of at least two distinct types
of randomly dispersed atoms. Our main tools are the reflection and transmission
coefficients for compactly supported single site perturbations of a periodic
background which we use to verify the necessary hypotheses of multi-scale
analysis. We show that non-reflectionless single sites lead to a discrete set
of exceptional energies away from which localization occurs.
