EPA recommends, in the latest update (2014) to the Exposure Factors Handbook, that the default estimate for soil and dust ingestion combined in children should be 200 mg/day, mentioning that this is an "upper-bound value" (and checking the references shows that this applies for children aged 3 to 6). But what would a best estimate be, and how uncertain is that? What uncertainty and variability distributions should be used in a probabilistic risk assessment? In the latest IRIS summary on acrylamide, EPA estimates the carcinogenic slope factor as 0.5 kg-day/mg. Again, how uncertain is that, and what value(s) should be used in a probabilistic risk assessment? These are the types of questions that require the detailed uncertainty analyses at which we excel. Various approaches are possible, but we prefer to start with the original data used in the derivation of point estimates, and proceed logically along the same pathway used in that derivation. Instead of concentrating on a single central or upper bound value, we account for uncertainty (and variability where necessary) in the models used in the derivation. Such an approach often leads to discovery of unstated assumptions in such derivations, in which case we look further and more deeply into theory and experiment, generalizing the approaches used, and introducing substantially more original data. Indeed, uncertainty analysis often forces explicit consideration of the underlying assumptions and models used in the derivation of single point estimates. For example, the uncertainty in carcinogenic slope factors is currently dominated by the uncertainty in interspecies extrapolation, even when accepting the assumptions required to resolve the validity of such extrapolations. We have recently evaluated the uncertainties involved and demonstrated that the typical approach used by regulatory agencies of selecting key experiments is arbitrary and in need of reform.