We have pet-formed Monte Carlo simulations of the properties of a NaCl (001) surface covered by full or partial layers of KCl, for coverages up to 5 monolayers (ML). A wide variety of structures of the film is found. For integer ML coverages we find the continuous, so-called floating mode rumple structure, as was previously found in the KBr/NaCl system. However, for a coverage of similar to 2.1 ML, we find a discrete structure of periodicity 3:4 of small regularly spaced KCl pyramids. It has the same scattering characteristics as the structure observed by Henzler et al. [Phys. Rev. B 52, 17 060 (1995)], but it is two-dimensional modulated, rather than the rowlike stacking fault structure proposed by Henzler et al. Also, at a coverage of similar to 0.8 ML there is a stable 3:4 structure. Other structures are found at intermediate coverages, corresponding to regular arrays of dislocation lines with periodicity 9:10. A further growth from such structures would give rise to growth of a similar to 5 degrees miscut KCl crystal relative to the NaCl lattice. The reciprocal space patterns corresponding to the continuous and the discrete film deformations are also calculated.