Hydrologists have been struggling over the past decades to improve rainfall-runoff models. As a consequence, models proposed 20-30 years ago still keep evolving as progress is made in the understanding of catchment hydrological behaviour. Here we present the GR4J model, a daily lumped rainfall-runoff model which is the result of a continuous improvement process over the last 15 years. The article provides the mathematical formulation of a new four-parameter version of the model. Model performance is assessed on a large sample of catchments: compared to other rainfall-runoff models, the GR4J performance is among the best ones. It also gives better results than the previous three-parameter model version, especially in the simulation of low flows. The tests indicate that a four-parameter structure corresponds to the maximum level of complexity that could be afforded in the model. Adding more free parameters did not bring significant improvements. The gain in model robustness with this new version should enhance the confidence in the practical use of this simple model for water engineering and resource management. The discussion underlines the potential limits introduced in the modelling process when one relies on a priori concepts in building a model structure and it stresses the value of large catchment samples to assess models.