The improved initialization inversion (3I) algorithms convert TIROS-N Operational Vertical Sounder (TOVS) observations from the NOAA polar orbiting environmental satellites into atmospheric temperature and water vapor profiles as well as cloud and surface properties. Because of their relatively high spectral resolution, infrared vertical sounders are especially useful for the identification of cirrus clouds. Differences in cirrus emissivity between the wavelengths 8.3 and 11.1 μm are used to retrieve ice crystal size; the radiative transfer model is based on the anomalous diffraction approximation applied to different crystal morphologies. We present sensitivity studies of ice crystal sizes estimated on a global scale to uncertainty factors in the retrieval as well as to assumptions in the model. On average, cirrus ice crystal mean maximum dimensions lie between 80 and 150 μm or effective ice crystal sizes between 35 and 45 μm. Correlations between estimated cirrus ice crystal mean maximum dimensions and cloud-top temperature seem to be positive in the tropics and midlatitude winter but depend on assumed temperature-dependent ice crystal morphology and size distribution function. These estimates can be helpful for the evaluation of general circulation models. With satellite measurements, one estimates mean ice crystal sizes mostly on the top of the cirrus clouds. However, when the clouds are thinner, the IR sounder can reach deeper into the cloud. Yet a quantitative relation between cloud thickness (effective cloud emissivity) and retrieval height inside the cloud has still to be investigated. ¿ 1999 American Geophysical Union