We study the relationship between precipitate morphology and superconductivity in K_xFe_1.6+ySe₂ single crystals grown by self-flux method. Scanning electron microscopy (SEM) measurements revealed that the superconducting phase forms a network in the samples quenched above iron vacancy order-disorder transition temperature T_s, whereas it aggregates into micrometer-sized rectangular bars and aligns as disconnected chains in the furnace-cooled samples. Accompanying this change in morphology the superconducting shielding fraction is strongly reduced. By post-annealing above T_s followed by quenching in room temperature water, the network recovers with a superconducting shielding fraction approaching 80% for the furnace-cooled samples. A reversible change from network to bar chains was realized by a secondary heat treatment in annealed samples showing a large shielding fraction, that is, heating above T_s followed by slow cooling across T_s. The large shielding fraction observed in K_xFe_1.6+ySe₂ single crystals actually results from an uniform and contiguous distribution of superconducting phase. Through the measurements of temperature dependent x-ray diffraction, it is found that the superconducting phase precipitates while the iron vacancy ordered phase forms together by cooling across T_s in K_xFe_1.6+ySe₂ single crystals. It is a solid solution above T_s, where iron atoms randomly occupy both Fe1 and Fe2 sites in the iron vacancy disordering status; and phase separation is driven by the iron vacancy order-disorder transition upon cooling. However, neither additional iron in the starting mixtures nor as-quenching at high temperatures can extend the miscibility gap to the KFe₂Se₂ side.