Abstract A bin (or spectral) model is developed to investigate the sensitivity of warm rain initiation to cloud condensation nuclei (CCN). It explicitly represents CCN with a formula whose parameters come from the Twomey relationship (or CCN measurements). By seamlessly integrating CCN activation and drop collection with thousands of bins, the model can replicate the effect of CCN on rain initiation, providing a benchmark to test the process parameterizations in rain initiation. The model is used to simulate two extreme cases with CCN parameters of maritime and continental clouds, respectively, where other actual cases usually lie between these two extreme cases. Its simulations show that rain can initiate within half an hour or less as observed in cumulus clouds. The fast rain initiation modeled is attributed mainly to a new process: the condensational conversion of cloud drops to raindrops via collision–coalescence initiators (or drops with radius between 28 and 100 μm). Since the new process is more important in rain initiation than the autoconversion of cloud drops to raindrops when large CCN exist, it is suggested that the process be parameterized into the weather and climate models to better represent CCN and subsequently remove the common bias of “too dense clouds.” Significance Statement The current weather and climate models represent aerosols via implicit parameterizations and have a bias of “too dense clouds.” Their implicit parameterizations of aerosols usually overlook (or misrepresent) some cloud processes. In this paper and its preceding part (Zeng and Li 2020) we proposed a new framework to explicitly parameterize one subset of aerosols: cloud condensation nuclei (CCN). To embody an explicit parameterization of CCN, we still need quantitative information to connect CCN activation and rain initiation, which motivates this study. In the study we developed an accurate microphysical model to simulate the growth of small CCN to large raindrops, providing information on the sensitivity of rain initiation to CCN. We performed many sensitivity simulations and found the condensational conversion of cloud drops to raindrops via collision–coalescence initiators is a vital process in warm rain initiation. Since the process has been overlooked by all the weather and climate models, the study suggests that the process be introduced in the weather and climate models to properly represent the fast warm rain initiation observed and subsequently remove the bias of “too dense clouds.”