Reactions of the elements within welded Ta containers at ∼600 °C followed by slow cooling give new A₈Tl₁₁Pd_x products from an apparently continuous encapsulation of Pd atoms into the pentacapped trigonal prismatic anions in the isotypic rhombohedral (R3̄c) A₈Tl₁₁ phases. All systems also produce other phases at x < 1 as well, the simplest being the cesium system in which only trigonal Pd₁₃Tl₉ is also formed. Cs₈Tl₁₁Pd_0.84(1) was characterized by single-crystal means as close to the upper x limit in that system (R3̄c, Z = 6, a = 10.610(1) Å, c = 54.683(8) Å). The Pd insertion causes an expansion of the D₃ host anion, particularly about the waist, to generate a trigonal bipyramidal PdTl₅ unit (d(Pd-Tl) ∼ 2.6-2.8 A) centered within a somewhat larger Tl₆ trigonal prism, the remainder of the Tl₁₁ cluster. Strong Tl cage bonding is retained. Extended Hückel calculations show significant involvement of all Tl 6s, 6p and Pd 4d, 5s, 5p orbital sets in the central and cage bonding. The last valence electron is considered to be delocalized in a conduction band, as in A₈Tr₁₁ examples, rather than occupying an antibonding e″ LUMO across a gap of ∼2.4 eV.