Infrared photoluminescence (PL) measurements were performed on (2ID-oriented superlattices with energy gaps in the range 110–495 meV. Most of the samples with thinner HgTe quantum wells displayed two PL peaks separated by Δhω ≈ 30–65 meV (which generally increased with decreasing well thickness). Both peak energies (Ep) sometimes varied gradually with location on the surface, and in one case three peaks of approximately equal spacing were observed in some locations. The data are consistent with a model which assumes the presence of randomly distributed islands having well thicknesses varying by approximately one monolayer. We find that Ahco and the variations of the spectra with temperature agree well with calculations based on this simple model.