Molecular mechanics calculations were used to compute the structural properties of a new type of very rigid tetradentate ligand for tetrahedral co-ordination geometries. The calculations indicate that the pendant arms of the disubstituted bispidine (3,7-diazabicyclo[3.3.1]nonane) backbone need to form six-membered chelate rings with the metal to allow a distorted tetrahedral geometry. Smaller rings lead to five- (trigonal bipyramidal) or six-co-ordinate (octahedral) transition-metal compounds. The quality of these predictions is supported by the experimentally determined structure of a cobalt(II) compound of the ligand with co-ordinated pyridine substituents (five-membered chelate rings) and an additional bidentate nitrate ligand. Comparison of the computed structures with the crystal structure of the cobalt(II) compound and with that of a ligand with methyl-protected phenyl substituents supports the rigidity of the bispidine backbone and indicates that rotation of co-ordinating side chains around a C–C single bond is the only flexibility in these ligands.