  The homoepitaxial growth of initially flat surfaces has so far always led to
surfaces which become rougher and rougher as the number of layers increases:
even in systems exhibiting ``layer by layer'' growth the registry of the layers
is gradually lost. We propose that pulsed glancing-angle sputtering, once per
monolayer, can in principle lead to layer-by-layer growth that continues
indefinitely, if one additional parameter is controlled. We illustrate our
suggestion with a fairly realistic simulation of the growth of a Pt (111)
surface, coupled with a simplified model for the sputtering process.
