A parametrization of cirrus clouds formed by homogeneous nucleation is improved so that it can be used more easily in general-circulation models (GCMs) and climate models. The improved parametrization is completely analytical and requires no fitting of parameters to models or measurements; it compares well with full microphysical model results even when monodisperse aerosol particles are used in the parametrization to determine cirrus ice-crystal number densities. However, the presence of ice nuclei in the atmosphere can modify the formation of cirrus clouds. If sufficient ice particles have been generated by heterogeneous nucleation, the saturation ratio of the air parcel will never reach that required for homogeneous nucleation. We calculate the critical number density of ice nuclei, above which homogeneous nucleation will be suppressed. The critical number density depends on the temperature, the updraught velocity, and the supersaturation at which ice nuclei activate. The theory points to key uncertainties in our observations of ice nuclei in the upper troposphere; for ice nuclei that activate at relatively low supersaturations, number density is more important than a precise knowledge of the activation supersaturation. Overall, the theory provides a general framework within which to interpret observations and the results of full microphysical cloud models. The theory can provide analytical test cases as benchmarks for the testing of models in development, and can be implemented itself into larger-scale atmospheric models, such as GCMs. Copyright © 2005 Royal Meteorological Society