An optimal estimation inverse method is presented which can be used to retrieve simultaneously vertical profiles of temperature and specific humidity, in addition to surface pressure, from satellite-to-satellite radio occultation observations of the Earth's atmosphere. The method is a nonlinear, maximum a posteriori technique which can accommodate most aspects of the real radio occultation problem and is found to be stable and to converge rapidly in most cases. The optimal estimation inverse method has two distinct advantages over the analytic inverse method in that it accounts for some of the effects of horizontal gradients and is able to retrieve optimally temperature and humidity simultaneously from the observations. It is also able to account for observation noise and other sources of error. Combined, these advantages ensure a realistic retrieval of atmospheric quantities. A complete error analysis emerges naturally from the optimal estimation theory, allowing a full characterization of the solution. Using this analysis, a quality control scheme is implemented which allows anomalous retrieval conditions to be recognized and removed, thus preventing gross retrieval errors. The inverse method presented in this paper has been implemented for bending angle measurements derived from GPS/MET radio occultation observations of the Earth. Preliminary results from simulated data suggest that these observations have the potential to improve numerical weather prediction model analyses significantly throughout their vertical range.