The structures of two new cubic {TnLa₃}Br₃ (Tn = Ru, Ir; I4₁32, Z = 8; Tn = Ru: a = 12.1247(16) Å, V = 1782.4(4) ų; Tn = Ir: a = 12.1738(19) Å, V = 1804.2(5) ų) compounds belonging to a family of reduced rare-earth metal halides were determined by single-crystal X-ray diffraction. Interestingly, the isoelectronic compound {RuLa₃}I₃ crystallizes in the monoclinic modification of the {TnR₃}X₃ family, while {IrLa₃}I₃ was found to be isomorphous with cubic {PtPr₃}I₃. Using electronic structure calculations, a pseudogap was identified at the Fermi level of {IrLa₃}Br₃ in the new cubic structure. Additionally, the structure attempts to optimize (chemical) bonding as determined through the crystal orbital Hamilton populations (COHP) curves. The Fermi level of the isostructural {RuLa₃}Br₃ falls below the pseudogap, yet the cubic structure is still formed. In this context, a close inspection of the distinct bond frequencies reveals the subtleness of the structure determining factors.