We report a theoretical investigation of the electronic structure and transport properties of eleven Zintl compounds including nine 122 phases (AMg₂X₂, AZn₂Sb₂ (A = Ca, Sr, Ba; X = Sb, Bi)) and two 212 phases (Ba₂ZnX₂ (X = Sb, Bi)). The electronic structures and electrical transport properties are studied using ab initio calculations and semi-classical Boltzmann theory within the constant relaxation time approximation. All the compounds are semiconducting. We find that the n-type 122 phases with the CaAl₂Si₂ structure type show better performance than p-type materials due to the multi-valley degeneracy with anisotropic carrier pockets at and near the conduction band minimum. The pocket anisotropy is beneficial in achieving high conductivity and Seebeck coefficient simultaneously. This mechanism yields substantial improvement in the power factor. The general performance of 212 phases is inferior to that of the 122 phases, with the Ba₂ZnSb₂ compound showing better performance.