We note that the zero bias conductance peak observed in tunneling into the [110] surface of adx2−y2superconductor has a width that is independent of disorder either in the bulk or at the surface. This remarkable property is accounted for qualitatively in terms of the tunneling into surface bound states in the superconductor which have widths that depend strongly on the momentum of the surface bound state. ©1999 American Institute of Physics.