We review the concept and the evolution of bandgap and wavefunction engineering, the seminal contributions of Dr. Chemla to the understanding of the rich phenomena displayed in epitaxially grown quantum confined systems, and demonstrate the application of these concepts to the colloidal synthesis of high quality type-II CdTe/CdSe quantum dots using successive ion layer adsorption and reaction chemistry. Transmission electron microscopy reveals that CdTe/CdSe can be synthesized layer by layer, yielding particles of narrow size distribution. Photoluminescence emission and excitation spectra reveal discrete type-II transitions, which correspond to energy lower than the type-I bandgap. The increase in the spatial separation between photoexcited electrons and holes as a function of successive addition of CdSe monolayers was monitored by photoluminescence lifetime measurements. Systematic increase in lifetimes demonstrates the high level of wavefunction engineering and control in these systems.