Attempts to devise techniques for rapidly calculating radiation transport in relatively simple shields has led to the development of two calculational models that are based on the use of cross-section sensitivity coefficients and are possible improvements over the traditional linear model. The two models, one an exponential model and the other a power model, were tested, along with the linear model, by applying them to 1- and 2-m-thick concrete slab problems in which the water content, reinforcing steel content, and composition of the concrete were varied. Comparing the results obtained with the three models with those obtained from an exact one-dimensional discrete ordinates transport calculation indicated that the exponential model, named the “BEST model” (for basic exponential shielding trend), is a particularly promising predictive tool for shielding problems dominated by exponential attenuation. When applied to a deep penetration sodium problem, the BEST model also yielded better results than did calculations based on second-order sensitivity theory.