Conditions are discussed for which the concentration, binding energy, and compensation of a set of impurities can be deduced from the temperature dependence of the thermal free‐carrier population. Improved methods for verifying the quality of a numerical fit to the mass‐action equations are illustrated with data for germanium doped with indium or mercury acceptors. The graphical methods illustrated permit a critical assessment of whether the data really conforms to the generally used equations, and how various forms of error or inapplicability can be observed. It is pointed out that these same techniques can be useful in analysis of thermal emission data under nonequilibrium conditions.