Abstract. A full two-moment microphysics parameterisation of the LIMA scheme (hereafter named LIMA v2.0) has been developed and successfully implemented in the Meso-NH cloud-resolving model. The novelty of the scheme is a set of prognostic equations of the number concentration of each precipitating ice category (snow-aggregates, graupel and hail), in complement to the prediction of the mass mixing ratios. As a result, new microphysical conversion rates are introduced and explicitly computed using the size distributions of the hydrometeors. The new LIMA v2.0 scheme has been tested for an idealized deep convection case against the original LIMA scheme characterized by an empirical number concentration-mixing ratio relationship applied to the precipitating ice. Inclusion of number concentration equations for the snow-aggregates and graupel significantly alters the microphysical structure and dynamical evolution of the simulated supercell. When comparing to the results obtained with the previous version of LIMA, the new v2.0 of the scheme tends to increase the pristine ice mixing ratio, to decrease the other ice hydrometeors, and to enhance the feedbacks between raindrops and the ice phase. The new scheme is also more efficient to produce earlier raindrops at ground level and to reduce hail precipitation.