The sensitivity of a cumulus parameterization scheme (CPS) to a representation of precipitation production is examined. To do this, the parameter that determines the fraction of cloud condensate converted to precipitation in the simplified Arakawa–Schubert (SAS) convection scheme is modified following the results from a cloud-resolving simulation. While the original conversion parameter is assumed to be constant, the revised parameter includes a temperature dependency above the freezing level, which leads to less production of frozen precipitating condensate with height. The revised CPS has been evaluated for a heavy rainfall event over Korea as well as medium-range forecasts using the Global/Regional Integrated Model system (GRIMs). The inefficient conversion of cloud condensate to convective precipitation at colder temperatures generally leads to a decrease in precipitation, especially in the category of heavy rainfall. The resultant increase of detrained moisture induces moistening and cooling at the top of clouds. A statistical evaluation of the medium-range forecasts with the revised precipitation conversion parameter shows an overall improvement of the forecast skill in precipitation and large-scale fields, indicating importance of more realistic representation of microphysical processes in CPSs.