It is shown that a commensurate square monolayer solid of Kr/NaCl(001) can be stabilized with a model incorporating a rather large energy corrugation amplitude. Then a square bilayer is formed under a compression and preempts the formation of an incommensurate triangular monolayer lattice. The lattice dynamics of the commensurate monolayer may be complex, because the modeling admits the possibility that it has a (2 × 2) unit cell with four Kr atoms.