New state-of-the-art methodology is described to analyze the Atmospheric Infrared Sounder/Advanced Microwave Sounding Unit/Humidity Sounder for Brazil (AIRS/AMSU/HSB) data in the presence of multiple cloud formations. The methodology forms the basis for the AIRS Science Team algorithm, which will be used to analyze AIRS/AMSU/HSB data on the Earth Observing System Aqua platform. The cloud-clearing methodology requires no knowledge of the spectral properties of the clouds. The basic retrieval methodology is general and extracts the maximum information from the radiances, consistent with the channel noise covariance matrix. The retrieval methodology minimizes the dependence of the solution on the first-guess field and the first-guess error characteristics. Results are shown for AIRS Science Team simulation studies with multiple cloud formations. These simulation studies imply that clear column radiances can be reconstructed under partial cloud cover with an accuracy comparable to single spot channel noise in the temperature and water vapor sounding regions; temperature soundings can be produced under partial cloud cover with RMS errors on the order of, or better than, 1 K in 1-km-thick layers from the surface to 700 mb, 1-km layers from 700-300 mb, 3-km layers from 300-30 mb, and 5-km layers from 30-1 mb; and moisture profiles can be obtained with an accuracy better than 20% absolute errors in 1-km layers from the surface to nearly 200 mb.