A family of tetrahedral mononuclear Co-III complexes with the cytosine nucleobase ligand is used as the playground for an in-depth study of the effects that the nature of the ligand, as well as their noninnocent distortions on the Co(II) environment, may have on the slow magnetic relaxation effects. Hence, those compounds with greater distortion from the ideal tetrahedral geometry showed a larger-magnitude axial magnetic anisotropy (D) together with a high rhombicity factor (E/D), and thus, slow magnetic relaxation effects also appear. In turn, the more symmetric compound possesses a much smaller value of the D parameter and, consequently, lacks single-ion magnet behavior.