Model calculations are reported for the condensation of atomic three-layer solids of xenon adsorbed on the (111) face of silver and for the condensation of xenon and of neon adsorbed on the basal-plane surface of graphite. The trilayers are found to be stable with respect to the formation of the three-dimensional solid of the adsorbate. For xenon the margin of stability in chemical potential energy is small compared with the triple-dipole energy and is of the same order as estimates for higher-order many-body dispersion energies. The relation of these calculations to experiments and calculations on multilayers is discussed.