High-quality single crystals of R2-xCexCuO4-y (R = Nd, Sm) were prepared over a range of Ce dopings x using CuO flux. By optimizing the growth conditions, free standing platelet single crystals as large as 10 X 10 X 0.1 mm3 were obtained reproducibly. TEM and SEM analyses verified that the crystals were single-phase with uniform Ce distribution. Both resistivity and magnetization showed sharp superconducting transitions (DELTA-T < 1 K) for x = 0.15. Because of the improved quality, the crystals are suitable for a definitive study of intrinsic properties. Details of the methods, post-growth annealing, and characterization of the crystals will be described.