The new tetragonal phases La3In4Ge and La3InGe are obtained from high-temperature reactions of the elements in welded Ta followed by annealing. The structures of both were established by single-crystal X-ray diffraction in tetragonal space group 14/mcm (Z = 4 and 16, a = 8.5165(3) and 12.3083(2) Angstrom, c = 11.9024(4) and 16.0776(4) Angstrom, respectively). La3In4Ge contains layers or slabs of three-connected indium built of puckered 8-rings and 4-rings, or of squashed tetrahedra ("butterflies") interlinked at all vertices, and these are separated by layers of La and isolated Ge. The phase is deficient of being a Zintl phase by three electrons per formula unit and is better described in terms of an alternate optimized and delocalized bonding picture and an open-shell metallic behavior for the In slabs. The more complex La3InGe, isostructural with Gd3Ga2, is also layered. This phase contains pairs of mixed-occupancy (0.75 In, 0.25 Ge) sites separated by 3.020 Angstrom, as well as isolated In and Ge atoms. The former appear to be fully reduced closed-shell atoms (relative to the bonded Ga dimers in Gd3Ga2) that are held in somewhat close proximity by cation matrix effects. The compound appears to be semiconducting and thus is a classical Zintl phase, (La+3)(3)In-5Ge-4 in the simplest oxidation state notation. High Coulomb energies are presumably important for the nature of the bonding and the stabilities of both compounds.