A series of mononuclear Dy complexes with the general formula [DyLz(salicylaldehyde)]·X·solvent (Lz = 6-pyridin-2-yl[1,3,5]triazine-2,4-diamine; X = OH (1·OH), Cl (2·Cl), Br (3·Br)) have been synthesized using mixed salicylaldehyde/pyridinyl-triazine ligands and discriminative counteranions. The Dy ion in these three complexes resides in a similar D coordination geometry with counteranions perturbing the coordination environment and bond lengths and angles in the lattice. Magnetostructural studies reveal that the asymmetric distribution of salicylaldehyde/pyridinyl-triazine ligands and the presence of discriminative counteranions result in the coexistence of large anisotropy and quantum tunneling of magnetization. The magnetic anisotropy is dominated by the axial ligand field with short Dy-O distances and large ∠O-Dy-O angles, while the quantum tunneling relaxation is probably dictated by the π-π stacking of the Lz ligands, which induces an axial constriction of the coordinating plane. Ab initio calculations substantiate the diversity of the magnetic behaviors in these complexes and highlight the importance of axial ligand field with short Dy-O distances, large ∠O-Dy-O angles and less ligand stacking in these pseudo-D-symmetrical single-molecule magnets.