Three new Zintl phases, Na11Ca2Al3Sb8, Na4CaGaSb3, and Na15Ca3In5Sb12, have been synthesized by solid-state reactions, and their structures have been determined by single-crystal X-ray diffraction. Na11Ca2Al3Sb8 crystallizes with its own structure type (Pearson index oP48) with the primitive orthorhombic space group Pmn21 (No. 31). The structure is best viewed as [Al3Sb8](15) units of fused AlSb4 tetrahedra, a novel type of Zintl ion, with Na+ and Ca2+ cations that solvate them. Na4CaGaSb3 also crystallizes in its own type with the primitive monoclinic space group Pc (No. 7; Pearson index mP36), and its structure boasts one-dimensional [GaSb3](6) helical chains of corner-shared GaSb4 tetrahedra. The third new compound, Na15Ca3In5Sb12, crystallizes with the recently reported K2BaCdSb2 structure type (space group Pmc21; Pearson index oP12). The Na15Ca3In5Sb12 structure is based on polyanionic layers made of corner-shared InSb4 tetrahedra. Approximately one-sixth of the In sites are vacant in a statistical manner. All three structures exhibit similarities to the TiNiSi structure type, and the corresponding relationships are discussed. Electronic band structure calculations performed using the tight-binding linear muffin-tin orbital atomic sphere approximation method show small band gaps for all three compounds, which suggests intrinsic semiconducting behavior for these materials.