The synthesis, structure, and properties of the ordered double perovskites Sr2FeOsO6, Ca2FeOsO6, and SrCaFeOsO6 are reported. The latter two compounds have monoclinic P21/n symmetry and a(-)a(-)b(+) tilting of the octahedra, while Sr2FeOsO6 is tetragonal with I4/m symmetry and a(0)a(0)c(-) tilting. Magnetic measurements indicate and neutron powder diffraction studies confirm that Ca2FeOsO6 is a ferrimagnet with a Curie temperature of 350 K. The ferrimagnetism is retained if half of the Ca(2+) ions are replaced with larger Sr(2+) ions to form SrCaFeOsO6 (TC = 210 K). This substitution reduces the degree of octahedral tilting, but unlike most perovskites, the magnetic ordering temperature decreases as the Fe-O-Os bond angles approach a linear geometry. In contrast, Sr2FeOsO6 orders antiferromagnetically, as previously reported. X-ray absorption spectroscopy confirms the assignment of Fe(III) and Os(V) oxidation states for all three compounds. In these insulating double perovskites, the magnetic ground state is governed by a competition between the four-bond Fe-O-Os-O-Fe antiferromagnetic superexchange coupling of Fe(III) ions and the two-bond Fe-O-Os antiferromagnetic superexchange coupling between neighboring Fe(III) and Os(V) ions. When the Fe-O-Os bonds are linear, as they are in the c direction in Sr2FeOsO6, the four-bond coupling between Fe(III) ions prevails. The competition shifts in favor of antiferromagnetic coupling of Fe(III) and Os(V) as the Fe-O-Os bond angles bend in response to chemical pressure.