A comparison of the carcinogenic potency estimates for many chemicals reveals that different governmental agencies derive and use alternative estimates of a chemical's carcinogenic potency. This paper examines which steps in the process of deriving carcinogenic potency estimates (e.g., high to low dose extrapolation, bioassay choice, data set treatment, etc.) contribute to the differences within and between governmental agencies by comparing the details of the process of potency estimation for four chemicals (ethylene dibromide, polychlorinated biphenyls, tetrachloroethylene and tetrachlorodibenzo-$p$-dioxin). For three of these four chemicals all agencies used similar high to low dose extrapolation models and most of the incompatibility arose from selection and treatment of bioassay results. The comparison suggests that an inverse relationship exists between the potential contribution of a parameter to incompatibility and its actual contribution; the existing incompatibility between agencies represented by existing differences in potency estimates is dwarfed by potential incompatibility; and, some but not all, of the incompatibility can be reduced.