A new method for the preparation of core/shell semiconductor nanocrystals of the A(II)B(VI) family is described, which involves the use of safe and cheap reagents at each synthesis stage, namely cadmium oxide as the Cd source and zinc stearate as the Zn source. It enables the fabrication of highly luminescent CdSe/ZnSe core/shell nanocrystals exhibiting a polydispersity <10%. In addition, a new double shell system is presented-CdSe/ZnSe/ZnS. An intermediate shell of ZnSe between the CdSe core and the outer shell of ZnS significantly lowers the lattice mismatch parameter assuring in this manner a ''smooth'' passage between the two crystallographically different components (CdSe and ZnS). At the same time the outer ZnS shell improves the charge carrier confinement in the core due to its larger band gap as compared to ZnSe. Photoluminescence spectroscopy of the CdSe/ZnSe/ZnS nanocrystals corroborates these arguments, as a significant increase in the fluorescence intensity is observed relatively to the CdSe/ZnSe and CdSe/ZnS systems.