  We show that one-dimensional Schr{\"o}dinger operators whose potentials arise
by randomly concatenating words from an underlying set exhibit exponential
dynamical localization (EDL) on any compact set which trivially intersects a
finite set of critical energies. We do so by first giving a new proof of
spectral localization for such operators and then showing that once one has the
existence of a complete orthonormal basis of eigenfunctions (with probability
one), the same estimates used to prove it naturally lead to a proof of the
aforementioned EDL result. The EDL statements provide new localization results
for several classes of random Schr{\"o}dinger operators including random
polymer models and generalized Anderson models.
