The low-temperature reduction of YBaCo2O5 and LaBaCo2O5 with NaH to form YBaCo2O4.5 and YBaCo2O4.25, respectively, demonstrates that the structures of anion-deficient materials formed by such topotactic reductions can be directed by the ordering and identity of the A-site cations. YBaCo2O4.5 adopts a structure consisting of a corner-shared network of square-based pyramidal CoO5 and distorted tetrahedral CoO4 units. The structure of LaBaCoO4.25 is more complex, consisting of an array of square-based pyramidal CoO5, distorted tetrahedral CoO4, and square planar CoO4 units. Magnetic susceptibility and variable-temperature neutron diffraction data reveal that YBaCo2O4.5 adopts a G-type antiferromagnetically ordered structure below T-N similar to 280 K. LaBaCo2O4.25 also adopts antiferromagnetic order (T-N similar to 325 K) with ordered moments consistent with the presence of square-planar, low-spin, s = 0, Co(I) centers. A detailed analysis reveals that the different anion vacancy ordered structures adopted by the two REBaCo2O5-x phases are directed by the relative sizes and ordering of the La3+ and Y3+ cations. This suggests that ordered arrangements of A-cations can be used to direct the anion vacancy order in topotactically reduced phases, allowing the preparation of novel metal-oxygen networks containing unusual transition metal coordination environments.