Rainfall prediction by weather forecasting models is strongly dependent on the microphysical parametrization being utilized within the model. As forecasting models have become more advanced, they are more commonly using double-moment bulk microphysical parametrizations. While these double-moment schemes are more sophisticated and require fewer a priori parameters than single-moment parametrizations, a number of parameter values must still be fixed for quantities that are not Prognosed or diagnosed. Two such parameters, the width of the rain drop size distribution and the choice of collection efficiencies between liquid hydrometeors, are examined here. Simulations of deep convective storms were performed in which the collection efficiency dataset and the a priori width of the rain drop size distribution (RSD) were individually and simultaneously modified. Analysis of the results show that the a priori width of the RSD was a larger control on the total accumulated precipitation (a change of up to 75% over the typical values tested in this article) than the choice of collection efficiency dataset used (a change of up to 10%). Changing the collection efficiency dataset produces most of the impacts on precipitation rates through changes in the warm rain process rates. On the other hand, the decrease in precipitation with narrowing RSDs occurs in association with the following processes: (a) decreased rain production due to increased evaporation, (b) decreased rain production due to decreased ice melting, and (c) slower raindrop fall speed which leads to longer residency times and changes in rain self-collection. These results add to the growing body of work showing that the representation of hydrometeor size distributions is critically important, and suggests that more work should be done to better represent the width of the RSD in models, including further development of triple-moment and bin schemes.