The photoluminescence (PL) quantum yield (QY) of CdSe nanocrystals during their growth under a given set of initial conditions increases monotonically to a certain maximum value and then decreases gradually. Such a maximum is denoted as a PL "bright point", which does not always overlap with the minimum point of the PL peak width for the same reaction. The experimental results suggest that the existence of the PL bright point is a general phenomenon during the growth of semiconductor nanocrystals and likely is a signature of an optimal surface structure/reconstruction of the nanocrystals grown under a given set of initial conditions. The position of the bright point, the highest PL QY, the types of the bright points (sharp or flat), the sharpness of the PL peak, etc., were all strongly dependent on the initial Cd:Se ratio of the precursors in the solution. A large excess of the selenium precursor, with 5-10 times more selenium precursor than the amount of the cadmium precursor, was found necessary to achieve a high PL QY value and a narrow emission profile. The existence of the PL bright point and the sensitive temporal variation of the PL QY during the growth of semiconductor nanocrystals can explain the unpredictable nature and poor reproducibility of the PL properties of the as-prepared semiconductor nanocrystals observed previously. Furthermore, the knowledge gained in this study enabled us to reproducibly synthesize highly luminescent CdSe nanocrystals through a relatively simple and safe synthetic scheme. In a traditionally weak emission window for CdSe nanocrystals, the orange-red optical window, the PL QY of the as-prepared CdSe nanocrystals reached as high as 85% at room temperature, and the full width at half-maximum of the corresponding PL peak was as narrow as 23 nm, about 65-80 meV depending on the emitting position. The PL properties of the as-prepared CdSe nanocrystals are stable upon aging for at least several months. These as-prepared nanocrystals represent a series of best emitters that are highly efficient, highly pure in emission color, stable, and continuously tunable by simply varying the size of the nanocrystals.