that the existing experimental data (for fields of view imaged by STS containing tens of impurities) for resonance strength versus gap size are extremely noisy[@hoffmanthesis] and show no clear evidence for a continuous suppression of the resonance peak as the local gap size is increased, a characteristic of [*all*]{} the theoretical models discussed here. Improving these statistics, with hundreds rather than tens of impurities, and binning over a range of gap sizes, should enable more robust conclusions to be drawn. According to Ref. , some of the effects of interference may also be minimized by defining the strength of the resonance via an integral over a small energy window near the peak rather than simply by the value of the conductance at a fixed bias.

Fourth, both the Kondo scenario and the phase impurity scenario produce the same spatial pattern for the Zn resonance as observed in experiment, whereas the screened Coulomb impurity picture requires an assumption of a filter mechanism. If the existence or nonexistence of such a mechanism could be settled in the case of the small-gap regions, it would enable one to rule out at least one candidate. Refs. and proposed that this could be settled if 