The ab initio/IGLO/NMR method has been successfully applied to establish the structures of the three known isomers of nido-C4B7H11. The method confirms the previously proposed structure, nido-7,8,9,10-C4B7H11, 1a, as one of the three known isomers. Of four candidates considered for the second isomer, one of the previously proposed structures, nido-1,7,8,10-C4B7H11, 2b, is selected. Of four candidates considered for the third isomer, structure nido-2,7,9,10-C4B7H11, 3b, which had not been previously proposed, is established. The relative order of stability is 1a > 2b > 3b. A comparison of the relative energies of the nine cage structures considered in this study shows that, in complete agreement with previous empirically determined patterns, the most stable structures are those in which the carbons occupy low coordinate sites. This preference is more important than avoiding carbon-carbon connections.