The Submillimeter-Wave Cloud Ice Radiometer (SWCIR), developed by the Jet Propulsion Laboratory to fly on the NASA DC-8, has ten channels from four receivers at 183, 325, 448, and 643 GHz. The SWCIR is designed to retrieve upper tropospheric cloud ice water path (IWP) and median mass equivalent sphere diameter (Dme). This paper describes the retrieval algorithm developed for the SWCIR, results from retrieval simulations, and the rationale for choosing the SWCIR frequencies. The retrieval algorithm uses Bayes theorem to combine prior information about atmospheric properties with radiative transfer simulations. The algorithm uses a precalculated database of stochastic cirrus/atmospheric profiles and corresponding simulated SWCIR brightness temperatures. Statistics of cirrus microphysics are derived from in situ cloud probe data obtained during midlatitude winter and tropical field experiments, and include correlations between temperature, particle size, and ice water content. The Bayesian algorithm effectively interpolates between database cases that approximately match the observed SWCIR brightness temperatures. Retrieval experiments are performed for midlatitude winter ice clouds with the SWCIR viewing downward from 12 km and for tropical anvil cirrus with the SWCIR viewing upward from 10 km. Each experiment simulates SWCIR brightness temperatures (with 1 K added noise) from 10000 random cloud/atmosphere profiles. For clouds with IWP greater than 5 g/m2 (which contain 97% of the simulated total ice mass) the overall median retrieval error is about 30% for IWP and 15% for Dme. The effects of liquid clouds just below ice clouds and of nonspherical ice particle shapes are small.