We present single-crystal studies of Pd0.213Cd0.787 and Pd0.235Cd0.765, synchrotron powder studies of Pd1−xCdx, 0.755≥x≥0.800, and LDA-DFT and extended Hückel (eH) calculations on these or related phases. The two single-crystal structures have a, b, and c axis lengths of 9.9013(7), 14.0033(10), 37.063(24) and 9.9251(3), 14.0212(7), 60.181(3) Å, respectively and they crystallize in the space groups Ccme and F2mm, respectively (solved as (3+1)-dimensional crystals their most convenient superspace group is Xmmm(00γ)s00). The structures have two different structural components each with their own separate axis parameters. Powder data shows that the ratio of these separate axes (S/L) varies from 1.615 to 1.64, values near the golden mean (1.618). For Pd0.213Cd0.787, different Pd and Cd site occupancies lead to variation in the R factor from 2.6–3.6 %. The site occupancy pattern with the lowest R factor (among the 26 820 variants studied) is the exact site occupancy pattern predicted by LDA-DFT parameterized eH Mulliken charge populations. The phases can be understood through a chemical twinning principle found in γ-brass, the parent structure for the above phases (a relation with the MgCu2 Laves phase is also noted). This twinning principle can be used to account for Cd and Pd site preferences. At the same time there is a clean separation among the Cd and Pd atoms for the two separate chain types at height b=0 and 1/2. These results indicate that Cd:Pd stoichiometry plays a role in phase stability.