The key characteristic of single-molecule magnets (SMMs) is the anisotropy-induced blocking barrier, which should be as efficient as possible, i.e., to be able to provide long magnetic relaxation times at elevated temperatures. The strategy for the design of efficient SMMs on the basis of transition-metal complexes such as Mn12Ac is well established, which is not the case of complexes involving strongly anisotropic metal ions such as cobalt(II) and lanthanides (Ln). While strong intraionic anisotropy in the latter allows them to block the magnetization already in mononuclear complexes, the presence of several such ions in a complex does not result automatically in more efficient SMMs. Here, the magnetic blocking in the series of isostructural 3d-4f complexes Co(II)-Ln(III)-Co(II), Ln = Gd, Tb, and Dy, is analyzed using an originally developed ab initio based approach for the investigation of blocking barriers. The theoretical analysis allows one to explain the counterintuitive result that the Co-Gd-Co complex is a better SMM than terbium and dysprosium analogues. It turns out that the highly efficient magnetic blockage in the Co-Gd-Co complex results from a concomitant effect of unexpectedly large unquenched orbital momentum on Co(II) ions (ca. 1.7 μB) and the large spin on the gadolinium (S = 7/2), which provides a multilevel blocking barrier, similar to the one of the classical Mn12Ac. We conclude that efficient SMMs could be obtained in complexes combining strongly anisotropic and isotropic metal ions with large angular momentum rather than in polynuclear compounds involving strongly anisotropic ions only.