Colloidal type II CdTe/CdSe nanocrystals were synthesized by sequential addition of a tri-n-octylphosphine telluride (TOPTe)/TOP solution and several shell-precursor solutions to a CdO/TOP solution; the shell-precursor solutions consisted of CdO and TOPSe in TOP. For the growth of the CdTe core, the TOPTe/TOP solution was swiftly added to the CdO/TOP solution at a higher temperature (300 degrees C) than the growth temperature (250 degrees C). For the growth of the CdSe shell, in contrast, the CdO/TOPSe/TOP solution was slowly added to the CdTe/TOP solution at a lower temperature than the growth temperature (200-240 degrees C). The temporal evolution of the optical properties of the growing core-shell nanocrystals was monitored in detail. During the growth of the CdSe shell, the core-shell nanocrystals exhibited interesting changes in photoluminescence (PL) properties. The highest PL efficiency (approximately 38 %) was detected from core-shell nanocrystals with a CdSe shell thickness of 0.4-0.5 nm (indicated by TEM); the formation of the first monolayer is proposed. Our synthetic approach is well suited to a practical realization of engineering materials with bandgaps in the near-IR and IR spectral ranges.