Laboratory measurements at the AIDA cloud chamber and airborne in situ observations suggest that the homogeneous freezing thresholds at low temperatures are possibly higher than expected from the so-called “Koop line”. This finding is of importance, because the ice onset relative humidity affects the cirrus cloud coverage and, at the very low temperatures of the tropical tropopause layer, together with the number of ice crystals also the transport of water vapor into the stratosphere. Both the appearance of cirrus clouds and the amount of stratospheric water feed back to the radiative budget of the atmosphere. In order to explore the enhanced ice onset humidities, we re-examine the entire homogeneous ice nucleation process, ice onset, and nucleated crystal numbers, by means of a two-moment microphysics scheme embedded in the trajectory-based model (CLaMS-Ice) as follows: the well-understood and described theoretical framework of homogeneous ice nucleation includes certain formulations of the water activity of the freezing aerosol particles and the saturation vapor pressure of water with respect to liquid water. However, different formulations are available for both parameters. ... mehrHere, we present extensive sensitivity simulations testing the influence of three different formulations for the water activity and four for the water saturation on homogeneous ice nucleation. We found that the number of nucleated ice crystals is almost independent of these formulations but is instead sensitive to the size distribution of the freezing aerosol particles. The ice onset humidities, also depending on the particle size, are however significantly affected by the choices of the water activity and water saturation, in particular at cold temperatures ≲205 K. From the CLaMS-Ice sensitivity simulations, we here provide combinations of water saturation and water activity formulations suitable to reproduce the new, enhanced freezing line.