We have investigated the processes that control ice crystal nucleation in the upper troposphere using a numerical model. Nucleation of ice resulting from cooling was simulated for a range of aerosol number densities, initial temperatures, and cooling rates. In contrast to observations of stratus clouds, we find that the number of ice crystals that nucleate in cirrus is relatively insensitive to the number aerosols present. The ice crystal size distribution at the end of the nucleation process is unaffected by the assumed initial aerosol number density. Essentially, nucleation continues until enough ice crystals are present such that their deposition growth rapidly depletes the vapor and shuts off any further nucleation. However, the number of ice crystals nucleated increases rapidly with decreasing initial temperature and increasing cooling rate. This temperature dependence alone could explain the large ice crystal number density observed in very cold tropical cirrus. ¿American Geophysical Union 1994