The focus in the search for more reliable predictions in ungauged basins (PUB) has generally been on reducing uncertainty in watershed models (mainly their parameters). More recently, however, we seem to remember that the ultimate objective is not to define the parameters of a specific model but to understand the watershed: What behavior do we expect the ungauged watershed to exhibit? And what behavior should not occur in a particular ungauged watershed? The answers to these questions actually provide additional information that can be assimilated in watershed models for uncertainty reduction in PUB. This extension to hydrologic modeling approaches provides a quantitative link between watershed modeling and statistical hydrology as well as process hydrology that has to be explored. We witness a convergence of approaches-Bayesian, set theoretic, and optimization based-toward utilizing this link. The result is an opportunity for the (quantitative) dialog between modelers, statistical hydrologists, and experimentalists. We close our discussion of this development by presenting new and exciting research questions that we now have to address.