Light absorption by black carbon (BC) particles emitted from fossil fuel combustion depends on their size and how thickly they are coated with nonrefractory species such as ammonium, sulfate, nitrate, organics, and water. The cloud condensation nuclei (CCN) activation behavior of a particle depends on its dry size and the hygroscopicities of all the individual species mixed together. It is therefore necessary to represent both size and mixing state of aerosols to reliably predict their climate-relevant properties in atmospheric models. Here we describe and evaluate a novel sectional framework in the Model for Simulating Aerosol Interactions and Chemistry (box model), referred to as MOSAIC-mix, that represents the mixing state by resolving aerosol dry size (Ddry), BC dry mass fraction (WBC), and hygroscopicity (k). Using 10 idealized urban plume scenarios in which different types of aerosols evolve over 24 h under a range of atmospherically relevant conditions, we examine errors in CCN concentrations and optical properties with respect to the level of detail of the aerosol mixing state representation. We find that a small number of WBC and k bins can achieve significant reductions in the errors and propose a configuration with 24 Ddry bins, 2 WBC bins, and 2 k bins that give average errors of about 5% or less in CCN concentrations and optical properties, 3-4 times lower than those from size-only resolved (i.e., internally mixed) simulations. These results suggest that MOSAIC-mix is suitable for use in regional and global models to examine the effects of mixing state on aerosol-radiation-cloud feedbacks. Copyright © 2016 American Geophysical Union. All Rights Reserved.