We have conducted a systematic 57Fe Mössbauer study on BaR(Cu0.5Fe0.5)2O5+δ double perovskites with various oxygen contents and rare-earth elements (R = Lu, Yb, Y, Eu, Sm, Nd, and Pr). In samples based on R = Lu, Yb, Y, Eu, Sm the oxygen content remained at δ ≈ 0, upon reductive or oxidative heat treatments under normal pressure. The larger rare-earth elements, i.e. Nd or Pr, readily allowed for continuous oxygen content tuning up to δ ≈ 0.3. By employing high-pressure heat treatments higher oxygen contents were achieved for all samples. The Néel temperature of the samples was found to decrease with increasing amounts of oxygen entering the lattice. In high-pressure oxygenated samples the decrease was less severe indicating that despite the incorporation of oxygen a large amount of Fe still remains in the high-spin trivalent state. By using charge-neutrality arguments together with the relative intensities of the Mössbauer spectral components the average valences of Fe and Cu were obtained. Oxygenation under normal pressure led to a corresponding increase of the valence of Fe, while Cu remained divalent. Upon high-pressure heat treatment equal amounts of Fe3+ and Cu2+ were found to be oxidized to Fe5+ and Cu3+, respectively.