Numerical simulations of cirrus formation in the tropical tropopause layer (TTL) during boreal wintertime are used to evaluate the impact of heterogeneous ice nuclei (IN) abundance on cold cloud microphysical properties and occurrence frequencies. The cirrus model includes homogeneous and heterogeneous ice nucleation, deposition growth/sublimation, and sedimentation. Reanalysis temperature and wind fields with high-frequency waves superimposed are used to force the simulations. The model results are constrained by comparison with in situ and satellite observations of TTL cirrus and relative humidity. Temperature variability driven by high-frequency waves has a dominant influence on TTL cirrus microphysical properties and occurrence frequencies, and inclusion of these waves is required to produce agreement between the simulated and observed abundance of TTL cirrus. With homogeneous freezing only and small-scale gravity waves included in the temperature curtains, the model produces excessive ice concentrations compared with in situ observations. Inclusion of relatively numerous heterogeneous ice nuclei (NIN $ 100 L21) in the simulations improves the agreement with observed ice concentrations. However, when IN contribute significantly to TTL cirrus ice nucleation, the occurrence frequency of large supersaturations with respect to ice is less than indicated by in situ measurements. The model results suggest that the sensitivity of TTL cirrus extinction and ice water content statistics to heterogeneous ice nuclei abundance is relatively weak. The simulated occurrence frequencies of TTL cirrus are quite insensitive to ice nuclei abundance, both in terms of cloud frequency height distribution and regional distribution throughout the tropics.