Parameterizing deep convection at model resolutions of a few kilometers or less requires diverging from several simplifying assumptions valid at coarser resolutions. The separation or complementarity between the deep-convection scheme and the model cloud scheme must be addressed properly to prevent a double counting of some phenomena, account for evolution in time, and keep consistent results while approaching resolutions where deep convection can be treated explicitly (without parameterization). In this paper, the author formulates and tests a perturbation approach of the bulk mass-flux representation of deep convective updrafts and downdrafts. The subgrid deep-convection scheme represents only the effect of the unresolved part of the real updrafts, complementing an explicit part associated with the mean gridbox vertical velocity. Special attention is paid to the ordering and interactions of the moist parameterizations, the formulation of the closure and of the triggering, and the accounting of time evolution aspects. The multiresolution behavior of the scheme is assessed in the operational numerical prediction model ALARO [a version of the Action de Recherche Petite Echelle Grande Echelle-Aire Limitée Adaptation Dynamique Développement In- ternational (ARPEGE-ALADIN) operational limited area model with a revised and modular structure of the physical parameterizations]. Unlike most mass-flux schemes, the parameterized part gradually fades out when the model resolution is increased, allowing the results to approach those of an explicit treatment of deep convection.