A conceptual framework, within which the bulk recycling models could incorporate the effects related to an incomplete vertical mixing of water in the tropospheric column, is developed. As an example, the bulk model with the modified well-mixed atmosphere condition, incorporating the "fast recycling" process, is constructed. The model contains a tunable, spatially varying parameter K that characterizes the level of the incomplete vertical mixing effects. The simplified analytical models based on the modified well-mixed atmosphere condition are developed. The analysis of the simplified model results shows that the regional recycling ratio may depend significantly on the average of K, but it depends only slightly on the rate of variation of K, which indicates that models with a constant K can be used instead of the variable K model.