Luminescent copper indium sulfide (CIS) nanocrystals are a potential solution to the toxicity issues associated with Cd- and Pb-based nanocrystals. However, the development of high-quality CIS nanocrystals has been complicated by insufficient knowledge of the electronic structure and of the factors that lead to luminescence quenching. Here we investigate the exciton decay pathways in CIS nanocrystals using time-resolved photoluminescence and transient absorption spectroscopy. Core-only CIS nanocrystals with low quantum yield are compared to core/shell nanocrystals (CIS/ZnS and CIS/CdS) with higher quantum yield. Our measurements support the model of photoluminescence by radiative recombination of a conduction band electron with a localized hole. Moreover, we find that photoluminescence quenching in low-quantum-yield nanocrystals involves initially uncoupled decay pathways for the electron and hole. The electron decay pathway determines whether the exciton recombines radiatively or nonradiatively. The development of high-quality CIS nanocrystals should therefore focus on the elimination of electron traps.