Crystalline layers of a simple, monoatomic fluid on a corrugated surface are studied using the molecular dynamics method. The structure of the first adsorbed layer at monolayer and multilayer coverages is examined. We observe a lateral compression of the first layer of the adsorbate lattice for bilayer coverage, relative to the monolayer coverage. This compression is largely driven by adsorbate-substrate interactions, and is most pronounced when the monolayer is incommensurate with the underlying substrate lattice. The results are consistent with neutron diffraction data of n-alkane molecules on graphite. (C) 2002 Elsevier Science B.V. All rights reserved.