The concept of dynamic localization goes back to an observation reported by Dunlap and Kenkre in 1986: The wave packet of a single particle moving on a single-band tight-binding lattice endowed with only nearest-neighbor couplings remains perpetually localized when driven by a spatially homogeneous ac force, provided the amplitude and the frequency of that force obey a certain condition [1]. When trying to overcome the limitations of the model, it is comparatively straightforward to deal with an arbitrary form of the dispersion relation-thus abandoning the nearest-neighbor approximation-and with arbitrary time-periodic forces, thus doing away with the restriction to purely sinusoidal driving [2]. But in any real lattice system an external time-periodic force will induce interband transitions, and it is by no means obvious whether dynamic localization can survive when these come into play.