We use photoluminescence excitation to study the electronic spectrum of CdSe quantum dots ranging from ~12 to ~53 Å in radius. We follow the size evolution of ten quantum dot absorption features. Comparison of the spectra with theoretical predictions allows us to confidently assign six of these transitions. We discuss the most likely assignments for the remaining four. We find that the nhS3/21Se and nhS1/21Se transitions dominate the spectra, accounting for half of the observed features. Our size-dependent data exhibit two strong avoided crossings, demonstrating the importance of valence-band structure in the description of the excited states.