From resonant Raman scattering measurements under hydrostatic pressure the authors were able to identify both the strain-shifted longitudinal optical phonon of CdSe quantum dots with different average size embedded in a quaternary ZnCdMgSe material and a Mg-local dot mode due to interdiffusion from the barrier. They show that the large tunability of the light emission, which covers most of the visible spectrum, is not only due to a different degree of confinement but also to a size-dependent built-in strain. The frequency of the Mg mode allowed them also to roughly estimate the amount of Mg interdiffusion into the quantum dots.