An extended study of the superconducting and normal-state properties of various as-grown and post-annealed Rb_xFe_2-ySe₂ single crystals is presented. Magnetization experiments evidence that annealing of Rb_xFe_2-ySe₂ at 413 K, well below the onset of phase separation T_p ≃ 489 K, neither changes the magnetic nor the superconducting properties of the crystals. In addition, annealing at 563 K, well above T_p, suppresses the superconducting transition temperature T_c and leads to an increase of the antiferromagnetic susceptibility accompanied by the creation of ferromagnetic impurity phases, which are developing with annealing time. However, annealing at T = 488 K ≃ T_p increases T_c up to 33.3 K, sharpens the superconducting transition, increases the lower critical field, and strengthens the screening efficiency of the applied magnetic field. Resistivity measurements of the as-grown and optimally annealed samples reveal an increase of the upper critical field along both crystallographic directions as well as its anisotropy. Muon spin rotation and scanning transmission electron microscopy experiments suggest the coexistence of two phases below T_p: a magnetic majority phase of Rb₂Fe₄Se₅ and a nonmagnetic minority phase of Rb_0.5Fe₂Se₂. Both microscopic techniques indicate that annealing the specimens just at T_p does not affect the volume fraction of the two phases, although the magnetic field distribution in the samples changes substantially. This suggests that the microstructure of the sample, caused by mesoscopic phase separation, is modified by annealing just at T_p, leading to an improvement of the superconducting properties of Rb_xFe_2-ySe₂ and an enhancement of T_c.