The feasibility of retrieving water vapor profiles from downlooking passive microwave sounder data is demonstrated by usage of a retrieval algorithm which extends Bayesian optimal estimation. Special Sensor Microwave T-2 (SSM/T-2) downlooking sounder data, consisting of brightness temperature measurements sensitive to water vapor, are used together with total water vapor content data for computing tropospheric water vapor profiles. The significant nonlinearity in the cost function, an implication of the corresponding (nonlinear) radiative transfer equation, necessitates several extensions of the well-known optimal estimation inversion scheme. We supplemented the scheme by simulated annealing and iterative a priori lightweighting and obtained a powerful physical-statistical hybrid algorithm. Retrievals based on SSM/T-2 data were compared to atmospheric analyses of the European Center for Medium-Range Weather Forecasts (ECMWF). A statistical validation of the retrieved profiles is presented. The comparisons indicate an approximate accuracy of about 15 to 20 percent for relative humidity. ¿ 1999 American Geophysical Union