The failure to obtain agreement between the calculated and measured reflector savings in the Fast Exponential Experiment led to a study of the processes involved in obtaining spectral equilibrium in small, highly enriched systems. It was shown that the length of the equilibrium region was a sensitive function of the pedestal thickness and could be optimized for this assembly. Factors which were found to be significant are, as expected, the geometry and the spectrum of the source. Both the experimental results and the theoretically derived results are presented. The methods of collecting data and the methods of data analyses which proved most fruitful are also presented.