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We present a high-resolution synchrotron X-ray diffraction study of xenon adsorbed on single-crystal graphite for coverages of two, three and six monolayers. We observe the evolution of the lattice mismatch between the xenon overlayer and a square root 3* square root 3R30 degrees structure commensurate with the underlying substrate. In the case of the bilayer we see a first-order incommensurate-commensurate (IC-C) phase transition at 62.0 K+or-1.2 K, which we demonstrate is consistent with the layer closest to the substrate having locked into the commensurate sites. The role of substrate quality is discussed and we conclude that previous studies on relatively poorer substrates may have favoured equilibrium structures strongly influenced by the surface imperfections. The risk of an insufficiently equilibrated adsorbate is discussed in the context of the very slow kinetics we observe for multilayer xenon on high-quality substrates. For the three- and six-layer adsorbates we observe a systematic increase in lattice mismatch with film thickness and no indication of an incommensurate-commensurate transition. We conclude that the trilayer system consists of many distinct domains approximately 500 AA across, each of which has a random close packed structure.