  We present a new, short, self-contained proof of localization properties of
multi-dimensional continuum random Schr\"odinger operators in the fluctuation
boundary regime. Our method is based on the recent extension of the fractional
moment method to continuum models in by Aizenman et al, but does not require
the random potential to satisfy a covering condition. Applications to random
surface potentials and potentials with random displacements are included.
