When it comes to reducing the predictive uncertainty in hydrological studies, the easiest and perhaps most widely used approach perhaps consists in hiding those catchments which we cannot understand with our models, on the grounds that input or calibration data are 'most probably' of bad quality. If we agree with Beven [2001] who describes the modelling process as an attempt to map a catchment into a model space, using hypothesis to constrain the mapping, then is obvious that in the development and validation of a rainfall-runoff model we will encounter data that do not fit into this conceptual frame at all, especially when working with large datasets. The purpose of this communication is to focus on these catchments that many modellers consider as obvious 'outliers' and often discard out of their datasets, for they give very poor results (e.g., highly negative Nash-Sutcliffe values). We would like to address the following questions: What does characterize these 'tail-of-distribution' catchments? Can we find a method to screen out major data inconsistencies without checking data series one by one (i.e., distinguish between model failures and measurement errors)? Should we get rid of those outliers in the validation phase of a RR model? We present several tests that have been performed on a large dataset of 1000 French catchments, using three models: the monthly GR2M model [Mouelhi et al., 2006], the daily GR4J model [Perrin et al., 2003], and the hourly GR4H model [Mathevet, 2005]. The main issues that we address here mainly deal with water balance closure from the surface hydrologist's point of view: the initialization of RR models for humid catchments, the problem of groundwater-dominated catchments; long-term, interannual behaviors; and intercatchment groundwater flows, and also the limits of NS criterion for both intermittent and groundwater-dominated catchments. Last, we discuss the implications of a 'rehabilitation' of outlier catchments for a realistic assessment of predictive uncertainty in rainfall-runoff modelling.