Structure analysis using X-ray and neutron powder diffraction and elemental mapping has been used to demonstrate that nominal A-site deficient Sr2−xFeMoO6−δ (0 ≤ x ≤ 0.5) compositions form as Mo-rich Sr2Fe1−yMo1+yO6 (0 ≤ y ≤ 0.2) perovskites at high temperatures and under reducing atmospheres. These materials show a gradual transition from the Fe and Mo rock salt ordered double perovskite structure to a B-site disordered arrangement. Analysis of the fractions of B–O–B’ linkages revealed a gradual increase in the number of Mo–O–Mo linkages at the expense of the ferrimagnetic (FIM) Fe–O–Mo linkages that dominate the y = 0 material. All samples contain about 10–15% antiferromagnetic (AF) Fe–O–Fe linkages, independent of the degree of B-site ordering. The magnetic susceptibility of the y = 0.2 sample is characteristic of a small domain ferrimagnet (Tc [similar] 250 K), while room temperature neutron powder diffraction demonstrated the presence of G-type AF ordering linked to the Fe–O–Fe linkages (mFe = 1.25(7)μB). The high temperature thermoelectric properties are characteristic of a metal with a linear temperature dependence of the Seebeck coefficient, S (for all y) and electrical resistivity ρ (y ≥ 0.1). The largest thermoelectric power factor S2/ρ = 0.12 mW m−1 K−1 is observed for Sr2FeMoO6 at 1000 K.