An extended study of the superconducting and normal-state properties of various as-grown and post-annealed RbxFe2−ySe2 single crystals is presented. Magnetization experiments evidence that annealing of RbxFe2−ySe2 at 413 K, well below the onset of phase separation Tp≃489 K, neither changes the magnetic nor the superconducting properties of the crystals. In addition, annealing at 563 K, well above Tp, suppresses the superconducting transition temperature Tc 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≃Tp increases Tc 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 Tp: a magnetic majority phase of Rb2Fe4Se5 and a nonmagnetic minority phase of Rb0.5Fe2Se2. Both microscopic techniques indicate that annealing the specimens just at Tp 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 Tp, leading to an improvement of the superconducting properties of RbxFe2−ySe2 and an enhancement of Tc.