Quantum size-confined CH3NH3PbX3 (X = Br and I) perovskite nanoplatelets with remarkably high photoluminescence quantum yield (up to 90%) were synthesized by ligand-assisted re-precipitation. Thickness-tunability was realized by varying the oleylamine and oleic acid ligand ratio. This method allows tailoring the nanoplatelet thickness by adjusting the number of unit cell monolayers. Broadly tunable emission wavelengths (450-730 nm) are achieved via the pronounced quantum size effect without anion-halide mixing.