We report a series of 3d–4f complexes {Ln2Cu3(H3L)2Xn} (X=OAc−, Ln=Gd, Tb or X=NO3
−, Ln=Gd, Tb, Dy, Ho, Er) using the 2,2′‐(propane‐1,3‐diyldiimino)bis[2‐(hydroxylmethyl)propane‐1,3‐diol] (H6L) pro‐ligand. All complexes, except that in which Ln=Gd, show slow magnetic relaxation in zero applied dc field. A remarkable improvement of the energy barrier to reorientation of the magnetisation in the {Tb2Cu3(H3L)2Xn} complexes is seen by changing the auxiliary ligands (X=OAc− for NO3
−). This leads to the largest reported relaxation barrier in zero applied dc field for a Tb/Cu‐based single‐molecule magnet. Ab initio CASSCF calculations performed on mononuclear TbIII models are employed to understand the increase in energy barrier and the calculations suggest that the difference stems from a change in the TbIII coordination environment (C
4v versus Cs).