Excitation transfer pathways in colloidal core/barrier/shell nanomaterials were investigated in the CdSe/ZnS/CdSe system. Absorption of light in the outer CdSe shell results in emission from the band edge of the CdSe core. The CdSe quantum shell acts as a light harvester that indirectly increases the brightness of the CdSe quantum-dot core. Spectroscopic evidence suggesting that the CdSe core and shell are coupled by tunneling of excitons through the ZnS barrier is provided. Competition kinetic analysis shows that charge transport competes effectively with hole capture by pyridine at the outer CdSe shell and exciton relaxation within the outer CdSe shell.