This paper looks at hydrological prediction from the point of view of flood forecasting, and it focuses on methods based on a rainfall-runoff (RR) modelling approach. For years, the traditional approach to flood forecasting was to use simulation models as forecasting models, through a two-step strategy. The model would be calibrated once for all, and then updated/recalibrated in real-time to improve model forecasts, based on the last available runoff information. A common belief among hydrological modellers was that a rainfall-runoff model and the updating procedure used for its application in forecasting mode could be chosen independently, i.e. that any updating procedure could be applied to any rainfall-runoff model. In recent years, the apparition of data-driven approaches (with relatively good performances as forecasting models) demonstrated that a two-step approach was not an absolute requirement, and it suggested us to try a new calibration approach that would calibrate classical RR models directly in forecasting mode. This required modifying the RR model in order to make the updating procedure an integral part of the model. Here, we discuss the respective merits of one-step vs two-step calibration strategies, the changes in RR model required to make the one-step strategy possible, and we show on a large set of 188 catchments how the one-step strategy does reduce predictive uncertainty.