By introducing of various equivalents of PbTe into the layered framework of CsBi4Te6, the four new compounds CsPbBi3Te6 (1), CsPb2Bi3Te7 (2), CsPb3Bi3Te8 (3) and CsPb4Bi3Te9 (4), were discovered. The compounds adopt layered structures built up of anionic slabs of progressively increasing thickness. The [PbmBi3Te5+m]- (m = 1, 2, 3, 4) slabs in the four structures can be viewed as fragments excised from the PbTe-type structures with 4-, 5-, 6- and 7-monolayers, respectively. As prepared, these materials are off-stoichiometric and n-type conductors. We present preliminary results of the crystal structures and thermoelectric properties of these materials and classify them as members of the new homologous series CsPbmBi3Te5+m (m = 1 to 4).