The impact of high-frequency gravity waves on homogeneous-freezing ice nucleation in cold cirrus clouds is examined using parcel model simulations driven by superpressure balloon measurements of temperature variability experienced by air parcels in the tropical tropopause region. We find that the primary influence of high-frequency waves is to generate rapid cooling events that drive production of numerous ice crystals. Quenching of ice nucleation events by temperature tendency reversal in the highest-frequency waves does occasionally produce low ice concentrations, but the overall impact of high-frequency waves is to increase the occurrence of high ice concentrations. The simulated ice concentrations are considerably higher than indicated by in situ measurements of cirrus in the tropical tropopause region. One-dimensional simulations suggest that although sedimentation reduces mean ice concentrations, a discrepancy of about a factor of 3 with observed ice concentrations remains. Reconciliation of numerical simulations with the observed ice concentrations will require inclusion of physical processes such as heterogeneous nucleation and entrainment.