The nucleation and initial growth of ice crystals in cirrus clouds at low (<235 K) temperatures prevailing in the upper troposphere and in the tropopause region is theoretically considered. The analysis explains the dependence of the number density of ice crystals on the vertical velocity and temperature seen in numerical simulations of cirrus formation when the timescale of depositional growth of the pristine ice particles is fast compared to the timescale of the freezing event. In such cases, applicable in many situations, the number of crystals formed via homogeneous freezing of aqueous solution droplets is rather insensitive to details of the aerosol size distribution, but increases rapidly with updraft velocity and decreases with temperature. The derived parameterization is validated with parcel model simulations, and its applicability for use in climate models is discussed. The potential role of aerosol size and heterogeneous freezing processes in altering the predicted cirrus properties is briefly addressed.