Effective resonance cross sections used in the analysis of heterogeneous reactors have generally been obtained through the use of equivalence theory and/or integral transport theory. One fundamentally restrictive assumption common to equivalence theory and most integral transport methods is the flat-source approximation. The assessment of this approximation was recently completed and comprised the following: 1. comparison of the broad-group cross sections of 238U in the resolved resonance region using. a. the flat-source approximation b. the exact source distribution c. the rational approximation with a Levine-type factor 2. comparisons in (1) for three types of reactors. a. typical zero power reactor (ZPR) assembly b. liquid-metal fast breeder reactor commercial power station c. light-water power reactor. The main conclusion was that even though there were significant differences between the exactly calculated escape probabilities and those calculated with the flat-source approximation, additional differences between the general energy-dependent reciprocity and the energy-independent (but often erroneously applied as energy-dependent) reciprocity relation almost completely compensated for the error in the flat-source escape probabilities. Due to this unusual and somewhat unexpected compensating effect, the effective capture cross sections of 238U in the resolved resonance region, generated by the three methods stated above, were essentially the same.