[1] The extent to which the rain rate from shallow, liquid-phase clouds is microphysically influenced by aerosol, and therefore drop concentration N d perturbations, is addressed through analysis of the precipitation susceptibility, S o . Previously published work, based on both models and observations, disagrees on the qualitative behavior of S o with respect to variables such as liquid water path L or the ratio between accretion and autoconversion rates. Two primary responses have emerged: (i) S o decreases monotonically with increasing L and (ii) S o increases with L, reaches a maximum, and decreases thereafter. Here we use a variety of modeling frameworks ranging from box models of (size-resolved) collision-coalescence, to trajectory ensembles based on large eddy simulation to explore the role of time available for collision-coalescence t c in determining the S o response. The analysis shows that an increase in t c shifts the balance of rain production from autoconversion (a N d -dependent process) to accretion (roughly independent of N d ), all else (e.g., L) equal. Thus, with increasing cloud contact time, warm rain production becomes progressively less sensitive to aerosol, all else equal. When the time available for collision-coalescence is a limiting factor, S o increases with increasing L whereas when there is ample time available, S o decreases with increasing L. The analysis therefore explains the differences between extant studies in terms of an important precipitation-controlling parameter, namely the integrated liquid water history over the course of an air parcel's contact with a cloud.