Lattice-matched ZnCdSe2 concentric epilayer shells up to 50 Angstrom in thickness have been grown on InP core quantum dots (QDs). The quality of the epitaxially grown shells was monitored by absorption and emission spectra and transmission electron microscopy (TEM). Shell growth was shown to be controllable and was consistently accompanied by a large red shift of the absorption and emission spectra. This results from increased electron delocalization and, hence, lower confinement energy compared to core QDs with no shell. Core-shell nanocrystals also show higher quantum yields for emission since the interface of the QDs is better passivated and deep surface trap luminescence is converted into band-edge luminescence. Theoretical calculations of the electron probability density in these core-shell QDs were made using high-level self-consistent field and tight-binding methods; the theoretical results are consistent with the experimental results.