The role of heterogeneous ice nuclei in controlling the occurrence and properties of cirrus clouds in the tropical tropopause layer is examined with the help of a Lagrangian microphysical cirrus model that includes competition between insoluble and volatile aerosol particles during ice nucleation and small-scale temperature perturbations. The potential of ice nuclei to influence the moisture budget of air at entry to the stratosphere appears to be limited. Additional dehydration of up to 0.3 ppmv may occur, relative to 1.3 ppmv caused by pure homogeneous freeze-drying. In contrast, ice nuclei significantly enhance the frequency of occurrence of subvisible cirrus clouds, even when present at concentrations as low as 0.01 L-1. This is likely to be the largest effect of ice nuclei on cirrus near the tropical tropopause. Ice nuclei may also alter cloud radiative forcing by changing the ice water content, increasing the effective crystal radius, and decreasing the cloud lifetime.