We demonstrate that ${\mathrm{CdS}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Se}}_{\mathit{x}}$ nanocrystals embedded in glass suffer compressive strain which increases as the crystallite radius decreases. A model based on the dependence of the cluster surface free energy on the surface-to-volume ratio explains very well the observed blueshift of the phonon bands in the Raman spectra.