Constant particle number, density and temperature (N, ρ, T) Molecular-Dynamics simulations are used to study second layer promotion and melting in a complete monolayer of krypton deposited onto a graphite substrate. In order to study the vertical behavior of the system and its relationship to melting, artificial horizontal constraints are introduced and their effects are systematically monitored. We find that horizontally confining each atom within an impenetrable cylinder increases the melting temperature Tm and causes melting to be less dramatic. The results also suggest that there is a limiting case of there being no transition for a sufficiently small confining cylinder. Vertical excursions of the adsorbate atoms increase at the onset of melting. The system subsequently goes through a vertical transition with increasing temperature, including second layer promotion followed by extinction of the partial second layer and the presence of a sparsely populated first layer and a large population of desorbed atoms. Horizontal confinement stifles true second layer promotion, causing the atoms to spend less time in the second layer at a given temperature and resulting in a thermal blurring of the adlayer, suggesting that in-plane fluctuations are a necessary part of the layer promotion mechanism. Horizontal confinement also raises the temperature where the vertical transition occurs but does not affect its sharpness or temperature extent.