New observations on the effect of surface morphology (corrugation) on the structure of vapor-deposited ice are presented. Amorphous quartz and single-crystal Si(100) were used as substrates. Water was deposited on the bare substrates and oil the substrates covered with organized organic thin films (OOTF). By coating the substrates with mixed organic monolayers, controlled corrugation was achieved, without affecting the chemical nature of the surface, Information on the surface corrugation on different scales was obtained by atomic force microscopy and wettability measurement techniques. The ice phase was determined by in situ infrared absorption measurements, Correlation was observed between the surface roughness on a scale that is characteristic for the distance between ice nucleation centers and the deposited ice structure, Molecular dynamics simulations could reproduce the experimental observations and provide an insight into its origin.