A strong electron-hole exchange interaction (EI) in semiconductor nanocrystals (NCs) gives rise to a large (up to tens of meV) splitting between optically active ('bright') and optically passive ('dark') excitons. This dark-bright splitting has a significant effect on the optical properties of band-edge excitons and leads to a pronounced temperature and magnetic field dependence of radiative decay. Here we demonstrate a nanoengineering-based approach that provides control over EI while maintaining nearly constant emission energy. We show that the dark-bright splitting can be widely tuned by controlling the electron-hole spatial overlap in core-shell CdSe/CdS NCs with a variable shell width. In thick-shell samples, the EI energy reduces to <250 μeV, which yields a material that emits with a nearly constant rate over temperatures from 1.5 to 300 K and magnetic fields up to 7 T. The EI-manipulation strategies demonstrated here are general and can be applied to other nanostructures with variable electron-hole overlap.