A physically based parameterization of cirrus cloud formation by heterogeneous freezing is developed along with a novel method to compute associated nucleation rates. The analysis is restricted to immersion freezing, possibly the dominant pathway for heterogeneous cirrus formation under cold (1.3--1.4 triggers cirrus formation, cloud properties are not very susceptible to changes of IN properties, as in the case of homogeneous freezing. In contrast, much stronger indirect aerosol effects on cirrus clouds are possible if at least two types of IN with distinct freezing thresholds compete during the freezing process, most likely leading to a suppression of ice crystal concentrations.