A new approach is presented to the problem of specifying constraints on retrieval estimators used to calculate vertical temperature profiles from satellite measurements of upwelling radiance. An unsupervised classification scheme determines the typical shapes of temperature profiles that represent meteorologically significant events in some large ensemble of profiles. A data base for this purpose is developed, and a set of typical shape functions (TSFs) calculated to represent the sample. The TSFs are used to specify a radiance classifier which, given a radiance observation, defines the TSF class and thereby the constraints upon the retrieval estimator. An example is given, using simulated 15 μm data for the NOAA-6 TOVS. Preliminary calculations with synthetic radiance data indicate that an optimum inverse retrieval estimator using TSF-defined constraints results in rms differences that are approximately 50% better than those for a truncated eigenvector expansion regression estimator using zonally defined statistics; improvement in the region of the midlatitude tropopause is greater than 50%.