Single crystals of two new iodide-iodates, Bi-3[IO3](12)center dot Ag4I and Tb-3[IO3](12)center dot Ag4I, are synthesized in hydrothermal systems. The anionic parts in both iodide-iodates are characterized as a complex charged framework of isolated IO3 umbrella-like groups and large Bi(Tb)-O polyhedra similar to those previously found in La3[IO3](12)[IO3](Pb3O). Broad channels along the c-axis contain compensators: (Ag3I)(2+) umbrella-like groups and additional Ag+ ions which form Ag-4(4+) tetrahedral clusters augmented with I- halogen. New iodates possess significantly higher second-order nonlinear optical characteristics compared to the previously known lead-containing compounds REE3[IO3](12)-[IO3](Pb3O), REE = La, Pr, Nd. The difference is related to the polar ordering of umbrella-like (Ag3I)(2+) groups in the channels in the new iodide-iodate. Additionally, planar-coordinated Ag atoms add three Ag atoms in umbrellas forming [Ag4I](3+) polar clusters in the channels.