The regulations that currently govern repositories for spent fuel and high-level waste require demonstrations that are sometimes described as impossible to make. To make them will require an understanding of the current and the future phenomena at repository sites; it will also require credible estimates of the probabilities that the phenomena will occur in the distant future. Experts in many fields—earth sciences, statistics, numerical modeling, and the law—have questioned whether any amount of data collection can allow modelers to meet these requirements with enough confidence to satisfy the regulators. In recent years some performance assessments have begun to shed light on this question because they use results of actual site investigations. Although these studies do not settle the question definitively, a review of a recent totalsystem assessment suggests that compliance may be possible to demonstrate. The review also suggests, however, that the demonstration can be only at the “reasonable” levels of assurance mentioned, but not defined, in the regulations.