A systematic investigation is presented on the influence of Sn-substitution in the clathrate-I compound Ba₈Zn_xGe_46−x−ySn_y, particularly for the crystal structure and thermoelectric properties including electrical resistivity, Seebeck coefficient, and thermal conductivity. Two series of samples were prepared to explore the changes for different Sn-contents, (y), and to define the optimum Zn-content, (x), for Ba₈Zn_xGe_46−x−ySn_y. Sn-incorporation leads to a linear expansion of the unit cell parameters. Sn-atoms occupy the 6d and 24k positions of the clathrate type-I structure (SG Pmn, standardized setting). Whereas the electrical resistivity and the Seebeck coefficient modify only slightly compared to Ba₈Zn_xGe_46−x, the thermal conductivity is significantly decreased by the Sn-atoms incorporated into the clathrate-I framework. Furthermore the charge carrier mobility is larger and the effective mass (m* = 1.7 m_e) is much smaller than those of the ternary compound Ba₈Zn_xGe_46−x. The maximum thermoelectric figure of merit is improved by 80% and reaches ZT = 0.82 at 850 K for Ba₈Zn_7.66Ge_36.55Sn_1.79.