  We consider a quantum particle in a periodic structure submitted to a
constant external electromotive force. The periodic background is given by a
smooth potential plus singular point interactions and has the property that the
gaps between its bands are growing with the band index. We prove that the
spectrum is pure point--i.e. trajectories of wave packets lie in compact sets
in Hilbert space-- if the Bloch frequency is non-resonant with the frequency of
the system and satisfies a Diophantine type estimate, or if it is resonant.
Furthermore it is shown that the KAM method employed in the non-resonant case
produces uniform bounds on the growth of energy for driven systems.
