The energies of the lowest excited state of hexagonal and zinc-blende CdSe spherical quantum dots are calculated using empirical pseudopotentials of the bulk semiconductor. The lowest excited state energies computed for hexagonal clusters are in reasonable agreement with recent experiments. We predict that zinc-blende and hexagonal dots have nearly the same lowest exciton energy shifts down to very small dot sizes. We have found that small changes in the pseudopotentials can turn the lowest energy transitions of small particles into indirect gaps.