The ability of a particle to serve as a cloud condensation nucleus in the atmosphere is determined by its size, hygroscopicity and its solubility in water. Usually size and hygroscopicity alone are sufficient to predict CCN activity. Single parameter representations for hygroscopicity have been shown to successfully model complex, multicomponent particles types. Under the assumption of either complete solubility, or complete insolubility of a component, it is not necessary to explicitly include that component's solubility into the single parameter framework. This is not the case if sparingly soluble materials are present. In this work we explicitly account for solubility by modifying the single parameter equations. We demonstrate that sensitivity to the actual value of solubility emerges only in the regime of 2×10^−1–5×10^−4, where the solubility values are expressed as volume of solute per unit volume of water present in a saturated solution. Compounds that do not fall inside this sparingly soluble envelope can be adequately modeled assuming they are either infinitely soluble in water or completely insoluble.