This paper proposes effective extensions to the well-known Bayesian optimal estimation, allowing one to cope not only with the ill-posedness but also with the intrinsic nonlinearity of many geophysical inversion problems. We developed a physical-statistical retrieval algorithm, which combines nonlinear optimal estimation with further optimization techniques. Profiling of water vapor based on (synthetic) downlooking microwave sounder data as an example for a typical geophysical nonlinear optimization problem is used to demonstrate the skills of the algorithm. Starting with a nonlinear scalar penalty function derived from a Bayesian approach, the sensible guess of a priori information, the selection of useful probability density functions, the advantages of simulated annealing, and the utility of Monte Carlo methods are discussed. These techniques together furnish capability for retrieving state vectors, which depend on the data in a (highly) nonlinear manner. The sensible combination as implemented in the introduced hybrid algorithm can provide solutions to problems that could not be tackled with standard (linearized) inversion methods properly. ¿ 2000 American Geophysical Union