In a previous study, we have derived an approximate, physically based parameterization of cirrus cloud formation by homogeneous freezing, applying to a wide class of supercooled aerosols in the upper troposphere and tropopause region. In this study, the parameterization scheme is extended to include the effects of aerosol size on the freezing process in adiabatically rising air parcels. Aerosol size effects become important when the timescale of the freezing event is fast compared to the timescale of depositional growth of the pristine ice particles. The generalized parameterization scheme is validated with parcel model simulations and can directly be applied in models that do not explicitly resolve the ice nucleation process, such as cloud-resolving models, weather forecast models, and climate models. The relationship between aerosol and ice crystal number concentrations in cirrus clouds formed by homogeneous freezing is discussed. This relationship is much weaker than in liquid water clouds. It is shown that even freezing of enhanced levels of sulfate aerosol originating from strong volcanic eruptions is unlikely to exert a sensible influence on cirrus formation.