Design criteria to obtain slow magnetic relaxation are theoretically investigated for two-coordinate complexes of Dy(III). It is shown that large energy barriers to magnetic relaxation, Ueff, can be achieved in the absence of near-linearity and generally that any two-coordinate complex of Dy(III) is an attractive synthetic target that may possess Ueff > 1000 cm(-1). These large Ueff values are immediately diminished if axial ligation is disrupted by solvent coordination.