The adaptation of a convective parametrization to high resolution has been successfully performed, to a certain point, by refinements in the representation of the entrainment, detrainment and some other features of the original general-circulation-model oriented scheme. But, passing to resolutions below 10 km requires dispensing with some fundamental hypotheses, starting with quasi-equilibrium and the assumption of negligible up- and downdraught mesh fractions. A prognostic scheme has been used for the draughts’ vertical velocities and mesh fractions. The prognostic closure of the convective scheme has many benefits, but additional enhancements are required, starting with a coherent treatment of the cloud condensates and a more integrated combination of the different schemes producing condensation, cloud and precipitation.