Conditional chain-dependent processes are fit to time series of daily precipitation amounts given an index of large-scale atmospheric circulation (i.e., either below or above normal monthly mean sea level pressure). Precipitation data for January at several locations in California are analyzed. The two conditional daily models differ both in terms of the parameters of the occurrence process and of the intensity process. Each of these daily effects contributes to changes in the distribution of monthly total precipitation associated with the circulation index. The process induced by combining the conditional daily models produces a variance for monthly total precipitation much closer to the observed value than that for the corresponding unconditional chain-dependent model.