The problem of Prediction in Ungauged Basins (PUB) is intimately linked with the concept of regionalisation; namely the transfer of information from one catchment that is gauged to another that is not. But such regionalisation exercises can be dangerous and should be attempted only with great care. The present paper addresses what the authors believe to be one essential aspect of regionalisation: namely, the importance of considering only ‘top-down ’ models that are parametrically efficient (parsimonious) and fully ‘identifiable ’ from the available catchment data. We argue further that many mechanistic model parameters are more naturally defined in the context of continuous-time, differential equation models (normally derived by the application of natural ‘laws’, such as mass and energy conservation). As a result, there are advantages if such models are identified and estimated directly in this continuous-time, differential equation form, rather than being formulated and estimated as discrete-time models. The arguments presented in the paper are illustrated by an example in which the top-down, Data-Based Mechanistic (DBM) approach to modelling is applied to a set of precipitation-flow data. This involves the application of an advanced method of continuous-time transfer function identification and estimation; and the interpretation of this estimated model in physically meaningful terms, as required by the DBM modelling approach.