Numerical simulations of deep, intense continental tropical convection indicate that when the cloud tops extend more than a few kilometers above the liquid water homogeneous freezing level, ice nucleation due to freezing of entrained aqueous sulfate aerosols generates large concentrations of small crystals (diameters less than $simeq$20 ¿m). The small crystals produced by aerosol freezing have the largest impact on cloud-top ice concentration for convective clouds with strong updrafts but relatively low aerosol concentrations. An implication of this result is that cloud-top ice concentrations in high anvil cirrus can be controlled primarily by updraft speeds in the tops of convective plumes and to a lesser extent by aerosol concentrations in the uppermost troposphere. While larger crystals precipitate out and sublimate in subsaturated air below, the population of small crystals can persist in the saturated uppermost troposphere for many hours, thereby prolonging the lifetime of remnants from anvil cirrus in the tropical tropopause layer.