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New {TbCu₃} and {DyCu₃} single-molecule magnets (SMMs) containing a low-symmetry Ln^III center (shape measurements relative to a trigonal dodecahedron and biaugmented trigonal prism are 2.2–2.3) surrounded by three Cu^II metalloligands are reported. SMM behavior is confirmed by frequency-dependent out-of-phase ac susceptibility signals and single-crystal temperature and sweep rate dependent hysteresis loops. The ferromagnetic exchange interactions between the central Ln^III ion and the three Cu^II ions could be accurately measured by inelastic neutron scattering (INS) spectroscopy and modeled effectively. The excitations observed by INS correspond to flipping of Cu^II spins and appear at energies similar to the thermodynamic barrier for relaxation of the magnetization, ∼15–20 K, and are thus at the origin of the SMM behavior. The magnetic quantum number <i>M</i>_tot of the cluster ground state of {DyCu₃} is an integer, whereas it is a half-integer for {TbCu₃}, which explains their vastly different quantum tunneling of the magnetization behavior despite similar energy barriers