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Replacing a monoanionic cyclopentadienyl (Cp) ligand in dysprosium single-molecule magnets (SMMs) with a dianionic cyclobutadienyl (Cb) ligand in the sandwich complexes [(η 4 -Cb'''')Dy(η 5 -C 5 Me 4 t Bu)(BH 4 )] - (1), [(η 4 -Cb'''')Dy(η 8 -Pn † )K(THF)] (2) and [(η 4 -Cb'''')Dy(η 8 -Pn † )] - (3) leads to larger energy barriers to magnetization reversal (Cb''''=C 4 (SiMe 3 ) 4 , Pn † =1,4-di(tri-isopropylsilyl)pentalenyl). Short distances to the Cb'''' ligands and longer distances to the Cp ligands in 1-3 are consistent with the crystal field splitting being dominated by the former. Theoretical analysis shows that the magnetic axes in the ground Kramers doublets of 1-3 are oriented towards the Cb'''' ligands. The theoretical axiality parameter and the relative axiality parameter Z and Z rel are introduced to facilitate comparisons of the SMM performance of 1-3 with a benchmark SMM. Increases in Z and Z rel when Cb''' replaces Cp signposts a route to SMMs with properties that could surpass leading systems., (© 2022 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)