Microwave radiances that may be measured from satellite-borne radiometers operating at 37 GHz have been computed as a function of rainfall rates from horizontally finite precipitating clouds that contain both ice and liquid hydrometers. If is found that precipitating ice at the top of the cloud depresses brightness temperatures significantly. Detailed comparison between finite clouds and the equivalent sections of plane-parallel clouds are made. Footprint averaged brightness temperatures from finite clouds are found to deviate considerably from the sectioned plane-parallel approximation, especially for large rain rates. Better agreement is achieved if a plane-parallel source function is used in the finite cloud model. The effect of shape and orientation of the precipitating cells with respect to the satellite has also been considered. It is found that the largest errors introduced by plane-parallel theory besides the footprint-filling errors are encountered when precipitating cells have large fractions of their surface below the freezing level or contain large amounts of ice. ¿ American Geophysical Union 1988