The crystal structures of two members of the solid solution series Bi_6+δS_6+3δCl_6-3δ and of Ag_1.2Bi_17.6S₂₃Cl₈ have been determined by single-crystal X-ray diffraction at room temperature. Single-crystals used for the investigations were obtained from a reaction involving Bi₂S₃ and AgCl in the molar ratio 3:2 at 740 K. Bi_6+δS_6+3δCl_6-3δ compounds crystallize in the hexagonal space group P6₃/m (no. 176) with a=11.427(2) Å, c=4.071(1) Å, for δ=0.64, and a=11.540(2) Å, c=4.040(1) Å, for δ=0.86 (Z=1). The disordered structure of Bi_6+δS_6+3δCl_6-3δ is closely related to the ordered rhombohedral structure of Bi₄S₅Cl₂. It consists of parallel six-membered ring channels of face- and edge-sharing bicapped trigonal prisms around Bi atoms with additional Bi atoms on the central axes. Ag_1.2Bi_17.6S₂₃Cl₈ adopts the monoclinic space group C2/m (no. 12) with a=53.036(9) Å, b=4.030(1) Å, c=11.643(4) Å, β=94.4(1)°, Z=2. Ag_1.2Bi_17.6S₂₃Cl₈ adopts a new structure type that can be interpreted as a periodic layered intergrowth of modules from Bi_6+δS_6+3δCl_6-3δ and the pavonite homologue Ag_3xBi_5-3xS_8-6xCl_6x-1 (^{(2, x)}P) along [1 0 0]. The detailed geometrical analysis reveals a remarkable similarity of the interface in the three structures.