Anvil cirrus generated by deep convection covers large fractions of the tropics and has important impacts on the Earth's radiation budget and climate. In situ measurements made with high-altitude aircraft indicate a rapid transition in ice crystal size distributions and habits as anvil cirrus ages. We use numerical simulations to investigate the impact of high-frequency gravity waves on the evolution of anvil cirrus microphysical properties. The impacts of both monochromatic gravity waves and ubiquitous stochastic mesoscale temperature fluctuations are simulated. In both cases, the interplay between wave-driven temperature fluctuations, deposition growth/sublimation, and sedimentation causes accelerated removal of both small ice crystals (diameters less than about 10 μm) and large crystals (diameters larger than ≈30 μm). These changes are consistent with the observed evolution of anvil cirrus microphysical properties. The Kelvin effect (higher saturation vapor pressure over curved surfaces) is a critical factor in the anvil evolution, driving mass transfer from small to large ice crystals. The wave-driven decrease in ice concentration is much faster for typical anvil cirrus detrained at ≃11.5–12.5 km than for less frequent anvils at 15.5–17.5 km because of the strong temperature dependence of deposition growth and sublimation rates. The simulations also show that waves, along with the Kelvin effect, drive growth of mid-sized (5–20 μm) ice crystals, which is consistent with the observed transition to bullet rosette habits in aging anvil cirrus. We conclude that high-frequency gravity waves, which are generally not resolved in large-scale models, likely have important impacts on anvil cirrus microphysical properties and lifetimes.