Two structural forms of the tetradentate bispidine ligand (3,7-diazabicyclo[3.3.1]nonane, pyridine-substituted at C2 and C4), coordinated to CuI, are known: a pentacoordinate square pyramidal structure with an acetonitrile completing the coordination sphere, and a tetracoordinate distorted tetrahedral structure, where one of the pyridine groups is dissociated. Similar structures are observed in crystals of the CuI complexes of another tetradentate and two pentadentate bispidine ligands. The structural dynamics in the CuI coordination sphere of the four ligands are probed by 1H-NMR spectroscopy, supported by approximate density functional theory (DFT) calculations. DFT and NMR spectroscopy indicate that there is an additional isomeric form, and experimental as well as computational data lead to the conclusion that the potential energy surfaces are very flat with various shallow minima.