Abstract: This work presents a new model for the movement of granular matter. It is a synthesis of the Hadeler–Kuttler and of the Savage–Hutter models. The result is a 3×3 system of balance laws able to describe the deposition-erosion dynamics, as in the former model, while being compliant with energy dissipation, as in the latter one. First, the basic analytical properties of the new model are described. Then, several numerical integrations allow to compare the different models. The present model appears to provide better descriptions of granular matter behaviour, in particular as soon as the bed's slope changes sign and deposition–erosion phenomena are relevant.