Herein we report a dinuclear [(μ-mbpymNO){(tmh)3Dy}2] (1) single-molecule magnet (SMM) showing two nonequivalent DyIII centers, which was rationally prepared from the reaction of Dy(tmh)3 moieties (tmh = 2,2,6,6-tetramethyl-3,5-heptanedionate) and the asymmetric bis-bidentate bridging ligand 4-methylbipyrimidine (mbpymNO). Depending on whether the DyIII ions coordinate to the N^O or N^N bidentate donor sets, the DyIII sites present a NO7 ( D2 d geometry) or N2O6 ( D4 d) coordination sphere. As a consequence, two different thermally activated magnetic relaxation processes are observed with anisotropy barriers of 47.8 and 54.7 K. Ab initio calculations confirm the existence of two different relaxation phenomena and allow one to assign the 47.8 and 54.7 K energy barriers to the Dy(N2O6) and Dy(NO7) sites, respectively. Two mononuclear complexes, [Dy(tta)3(mbpymNO)] (2) and [Dy(tmh)3(phenNO)] (3), have also been prepared for comparative purposes. In both cases, the DyIII center shows a NO7 coordination sphere and SMM behavior is observed with Ueff values of 71.5 K (2) and 120.7 K (3). In all three cases, ab initio calculations indicate that relaxation of the magnetization takes place mainly via the first excited-state Kramers doublet through Orbach, Raman, and thermally assisted quantum-tunnelling mechanisms. Pulse magnetization measurements reveal that the dinuclear and mononuclear complexes exhibit hysteresis loops with double- and single-step structures, respectively, thus supporting their SMM behavior.