An atomistic direct diagonalization pseudopotential approach has been used to analyze the optical excitation spectra of CdSe quantum dots for up to 1.5 eV about the band gap. Good agreement is obtained with experiment for all the eight excitonic transitions, without resorting to fitting to the experimental data on dots. The observed excitonic transitions are identified in terms of specific pairs of valence and conduction single-particle states. For the lowest few transitions, the assignments agree with the conventional k.p effective-mass result, but this is not the case for the higher peaks. Indeed, we find in our atomistic approach that many more valence states exist within a given energy range than in the continuum k.p approach. Furthermore, we find that the mixing of even and odd angular momentum symmetry, disallowed in the contemporary simple k.p models, is actually permitted in the more general atomistic approach.