We report different approaches to the synthesis of size series of highly luminescent CdSe/CdS core-shell nanocrystals. The mixture of hexadecylamine (HDA)-trioctylphosphine oxide (TOPO)-trioctylphosphine (TOP) as stabilizing solvent was found to be very suitable for one-pot synthesis of nearly monodisperse CdSe nanocrystals followed by growing the CdS shell of a desired thickness. The obtained CdSe/CdS nanocrystals exhibited a narrow PL band (fwhm similar to27-35 nm) with reproducible room-temperature quantum yields as high as 50-85%. The emission color is tunable from green to red with increasing diameter of CdSe cores and/or thickness of the US shell. The possibility of preparing high-quality CdSe/CdS core-shell nanocrystals from the precursors cadmium acetate and H2S, which are more environmentally benign than conventional ones (e.g., dimethylcadmium) used in the organometallic synthesis of nanocrystals, was demonstrated. General aspects of the nanocrystal nucleation and growth as well as applicability of "greener" synthetic schemes for synthesis of core-shell nanocrystals are discussed.