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Resonance Raman excitation profiles have been measured for the longitudinal optical phonon in two sizes of CdS quantum dots and in CdSe/CdS core/shell quantum dots. In pure CdS, the resonance Raman cross section for the fundamental transition is sharply peaked around the lowest-energy excitonic transition and becomes weaker with higher-energy excitation even though the absorbance continues to increase to higher energies. This effect, also observed in earlier studies of CdSe quantum dots, is attributed largely to interferences among multiple excitonic transitions contributing to the resonance Raman polarizability. No variation in exciton-phonon coupling strength with exciton energy is required to explain the decrease in the ratio of the Raman cross section to absorption cross section at shorter wavelengths. In core/shell structures, the CdSe phonons are relatively strong when exciting on resonance with the lower excitonic transitions, in which the hole is largely localized to the CdSe core, but become nearly undetectable at excitation wavelengths >0.6 eV above the lowest exciton, where both electrons and holes are largely localized in the CdS shell. The CdS phonon Raman cross section exhibits a maximum 0.6-0.7 eV above the lowest exciton and then decreases at higher energies for the same reasons as in pure CdS.