A simple mathematical model is proposed for the formation of engine deposits and their removal with detergent additive packages. The model is phenomenological and is intended to provide a framework within which the often complex experimental observations can be understood; it does not aspire to be fully predictive or to provide insights into the physics and chemistry of deposit formation. It is applied to inlet-valve deposit formation and removal, and the results demonstrate that two fuels, which might look similar in terms of deposit formation tendency, in a fixed duration engine test, might respond quite differently to the same detergent package. Two additive packages that give identical results in a keep-clean experiment can show quite different clean-up capabilities. A package that has very good keep-clean capability might not show any ability to clean up dirty valves but will do so at higher dose rates. It is more likely that clean-up will be observed if the initial deposit weight is high. If the components of the detergent package decompose and leave their own deposits, the valves can become dirtier than with the base fuel alone. The dose response curve for such an additive package depends on the fractional decomposition rate with the dose rate and on how dirtily the additive decomposes. These predictions are qualitatively consistent with experience of these phenomena.