Narrow-gap semiconductors are very rare among intermetallic compounds. They appear only when two factors come together: strong hybridization of valence orbitals in the vicinity of the Fermi level and an appropriate number of valence electrons. Surprisingly, the IrIn3 family of intermetallics contains a number of semiconductors, including 17 e- FeGa3, RuGa3, OsGa3, and RuIn3, for which the d-p hybridization gap opens at the Fermi energy. We present comprehensive total energy electronic-structure calculations and crystal orbital Hamilton population analysis of the stable IrIn3-type compounds with semiconducting and metallic properties. The calculated electronic structures possess two pseudogaps and one real gap at the magic valence electron count of 15, 17, and 18 e- per formula unit. When the Fermi level is located in these gaps, the antibonding states are minimized. Total energies calculated for the isomorphous compounds suggest that the metallic state with 18 e- leads to a comparable or even higher thermodynamic stability than the semiconducting state with 17 e-.