Random blinking is a major problem on the way to successful applications of semiconducting nanocrystals in optoelectronics and photonics, which until recently had neither a practical solution nor a theoretical interpretation. An experimental breakthrough has recently been made by fabricating non-blinking Cd(1-x)Zn(x)Se/ZnSe graded nanocrystals [Wang et al., Nature, 2009, 459, 686]. Here, we (1) report an unequivocal and detailed theoretical investigation to understand the properties (e.g., profile) of the potential-well and the distribution of Zn content with respect to the nanocrystal radius and (2) develop a strategy to find the relationship between the photoluminescence (PL) energy peaks and the potential-well due to Zn distribution in nanocrystals. It is demonstrated that the non-square-well potential can be varied in such a way that one can indeed control the PL intensity and the energy-level difference (PL energy peaks) accurately. This implies that one can either suppress the blinking altogether, or alternatively, manipulate the PL energy peaks and intensities systematically to achieve a controlled non-random intermittent luminescence. The approach developed here is based on the ionization energy approximation and as such is generic and can be applied to any non-free-electron nanocrystals.