The compound types A1+xM3-2xBi7+xSe14, A1−xM3−xBi11+xSe20, A1−xM4−xBi11+xSe21 and A1−xM5−xBi11+xSe22 (A = K, Rb, Cs; M = Sn, Pb) form from reactions involving A2Se, Bi2Se3, M and Se. The single crystal structures reveal that they are all structurally related so that they all belong to the homologous series Am[M6Se8]m[M5+nSe9+n] (M = di- and trivalent metal), whose characteristics are three-dimensional anionic frameworks with tunnels filled with alkali ions. The building units that make up these structures are derived from different sections of the NaCl lattice. In these structures, the Bi and Sn (Pb) atoms are extensively disordered over the metal sites of the chalcogenide network, giving rise to very low thermal conductivity. These phases are all narrow gap semiconductors with 0.25 < Eg< 0.60 eV and many possess physico-chemical and charge transport properties suitable for thermoelectric investigations.