We report a two-step synthesis of highly luminescent CdS/ZnSe core/shell nanocrystals (emission quantum yields up to 50%) that can produce efficient spatial separation of electrons and holes between the core and the shell (type-II localization regime). Our synthesis involves fabrication of cubic-singony CdS core particles that are subsequently overcoated with a layer of ZnSe in the presence of surfactant-ligands in a noncoordinating solvent. Studies of different growth regime of the ZnSe shell indicate that one approach to obtaining high emission efficiencies is through alloying the CdS/ZnSe interface with CdSe, which leads to the formation of an intermediate ZnCdSe layer with a graded composition. We perform theoretical modeling of these core/shell nanocrystals using effective mass approximation and applying first-order perturbation theory for treating both direct electron-hole coupling and the core/shell interface-polarization effects. Using this model we determine the range of geometrical parameters of the core/shell structures that result in a type-II localization regime. We further applied this model to evaluate the degree of electron-hole spatial separation (quantified in terms of the electron-hole overlap integral) based on measured emission wavelengths. We also discuss the potential applicability of these nanocrystals in lasing technologies and specifically the possibility of single-exciton optical gain in type-II nanostructures.