Zintl phases are compounds that have shown promise for thermoelectric applications. The title solid–solution Zintl compounds were prepared from the elements as single crystals using a tin flux for compositions x = 0, 1, 2, and 3. Eu₁₁Cd₆Sb_12–xAs_x (x < 3) crystallize isostructurally in the centrosymmetric monoclinic space group C2/m (no. 12, Z = 2) as the Sr₁₁Cd₆Sb₁₂ structure type (Pearson symbol mC58). Efforts to make the As compositions for x exceeding ∼3 resulted in structures other than the Sr₁₁Cd₆Sb₁₂ structure type. Single-crystal X-ray diffraction indicates that As does not randomly substitute for Sb in the structure but is site specific for each composition. The amount of As determined by structural refinement was verified by electron microprobe analysis. Electronic structures and energies calculated for various model structures of Eu₁₁Cd₆Sb₁₀As₂ (x = 2) indicated that the preferred As substitution pattern involves a mixture of three of the six pnicogen sites in the asymmetric unit. In addition, As substitution at the Pn4 site opens an energy gap at the Fermi level, whereas substitution at the other five pnicogen sites remains semimetallic with a pseudo gap. Thermoelectric properties of these compounds were measured on hot-pressed, fully densified pellets. Samples show exceptionally low lattice thermal conductivities from room temperature to 775 K: 0.78–0.49 W/mK for x = 0; 0.72–0.53 W/mK for x = 1; and 0.70–0.56 W/mK for x = 2. Eu₁₁Cd₆Sb₁₂ shows a high p-type Seebeck coefficient (from +118 to 153 μ V/K) but also high electrical resistivity (6.8 to 12.8 mΩ·cm). The value of zT reaches 0.23 at 774 K. The properties of Eu₁₁Cd₆Sb_12–xAs_x are interpreted in discussion with the As site substitution.