We present a new algorithm for retrieving optical depth and liquid water content and effective radius profiles of nonprecipitating liquid water clouds using millimeter wavelength radar reflectivity and dual-channel microwave brightness temperatures. The algorithm is based on Bayes' theorem of conditional probability and combines prior information on cloud microphysics with the remote sensing observations. Prior probability distribution functions for liquid water clouds were derived from the second, third, and sixth moments of droplet size distributions measured by in situ aircraft probes in shallow tropical cumuli. The algorithm also calculates error bars for each retrieved parameter. To assess the algorithm, we perform retrieval simulations using radar reflectivity and brightness temperatures simulated from tropical cumulus fields calculated by a large eddy simulation model with explicit microphysics. These retrieval simulations show that the Bayesian algorithm has similar magnitude errors to current retrieval methods for liquid water content and liquid water path retrievals but has much smaller errors for effective radius and optical depth. We also perform retrievals on three months of data from the Atmospheric Radiation Measurement (ARM) Program's site on Nauru in the tropical west Pacific. For nonprecipitating liquid water clouds over Nauru during June--August 1999 we retrieve a mean optical depth of 9.2, mean liquid water content of 0.112 g/m3, and mean effective radius of 7.8 ¿m. The Bayesian method is a flexible approach to cloud profile remote sensing and could be expanded to other sites or cloud types.