The structural and magnetic properties of air sintered and Ar and O2 annealed La0.875Sr0.125Mn1−γO3+δ polycrystalline samples have been studied systematically. From the simultaneous refinement of room-temperature x-ray and neutron powder diffraction data, we have found that the crystal structure is orthorhombic (Pbnm, Z = 4; O) for the Ar annealed sample and rhombohedral (R\bar {3}c , Z = 2; R) for the air sintered and O2 annealed samples. At the O–R transition, the average Mn–O–Mn bond angle increases from 161.08(4)° (Ar) to 163.38(1)° (O2) and 163.64(1)° (air). Ar and O2 annealings cause a decrease of the Curie temperature Tc from 240(1) K (air) via 237(1) K (O2) to 192(1) K (Ar). The Tc is reduced by ~20% for the sample with O structure (Ar) as compared with that of the samples with R structure (air and O2). The decrease of Tc is explained by the decrease of total strength of magnetic interactions, due to the decreased \langle \mathrm {Mn\mbox {--}O\mbox {--}Mn}\rangle bond angle and increased \langle \mathrm {Mn\mbox {--}O}\rangle bond length, and by the decrease of number of nearest magnetic neighbours. The possible reasons for the decrease of the Mn site occupancy after Ar and O2 annealings and the sources of apparent excess oxygen are discussed. Thus we have shown that the actual distributions of cation vacancies in the A (La and Sr) and B (Mn) sublattices induced by the changes of Mn and oxygen contents through Ar and O2 annealings play an important role in the structural and magnetic properties. Comparing the Ar annealed with the air sintered sample, a decrease as small as ~2.2% of the relative oxygen content leads to a remarkably large (~20%) effect on Tc.