A new global precipitation retrieval algorithm for the millimeter-wave Advanced Microwave Sounding Unit is presented that also retrieves Arctic precipitation rates over surface snow and ice. This algorithm improves upon its predecessor by excluding some surface-sensitive channels and by reducing the number of principal components (PCs) used to represent those that remain. The training sets were also modified to better represent cold regions. The algorithm still incorporates conversion of brightness temperatures to nadir, spatial filtering to better detect pixels scattering near 54 GHz, PC filtering of surface effects, and use of separate neural networks trained with the fifth-generation National Center for Atmospheric Research/Penn State Mesoscale Model (MM5) for land and sea, where warm and cold ocean are now treated differently. The validity of the snowfall detections is supported by nearly coincident CloudSat radar observations, and the physics of the model is largely validated by the reasonable agreement in annual precipitation obtained for 231 globally distributed rain gauges, including many at latitudes where snowfall dominates. Observed annual global precipitation statistics are also presented to permit comparisons with other algorithms and sensors.