Supersaturation was found to play a pivotal role during nanoparticle-synthesis and its subtle variation helped achieve two prime objectives: (a) high photoluminescence quantum efficiency (PLQE) and (b) narrow size distribution, thereby obviating the need for post-preparative treatments. Degree of supersaturation of initial synthetic mixture was varied by changing the concentration of reagents while keeping their molar ratio constant at 1:2.5:0.5 for [Cd(2+)]:[cysteine]:[chalcogenide]. An eight-fold increase in supersaturation caused a sharp focusing of size distribution by 64% for CdS quantum dots (QDs). The as-prepared CdS and CdTe QDs were found to have size distribution as low as 4% at higher supersaturation. For a four-fold increase in supersaturation, PLQE of as-prepared CdTe QDs (4.3 nm) rose by 5 times to a remarkably high value of 54%. The focusing of size distribution with increasing supersaturation was found to work well even in the absence of any stabilizer. A substantial overlap of nucleation and growth was found at low supersaturation (0.5S(CdTe)), whereas a good separation of the two events is achieved at a higher supersaturation (4S(CdTe)). This study provides a simplified aqueous route for producing highly monodisperse, photoluminescent and biocompatible nanoparticles.