  We identify a duality transformation in one-dimensional hopping models that
relates propagators in general disordered potentials linked by an up-down
inversion of the energy landscape. This significantly generalises previous
results for a duality between trap and barrier models. We use the resulting
insights into the symmetries of these models to develop a real-space
renormalisation scheme that can be implemented computationally and allows
rather accurate prediction of propagation in these models. We also discuss the
relation of this renormalisation scheme to earlier analytical treatments.
