as Fig. \[fig4\], but with a filter mechanism applied as described in text. []{data-label="fig5"}](Fig4a.eps){width="1.0\columnwidth"}

We now recall that the correct spatial pattern can be recovered by employing the assumption of a blocking layer “filter",[@JXZhu:2000b; @IMartin:2002] which supposes that the tunneling path to the CuO$_2$ plane is not direct. We employ the simplest of these approaches,[@JXZhu:2000b] which assumes that the LDOS measured on any given site is actually the average of the LDOS on the four NN sites. In this case, as seen from Fig. \[fig5\] the correct spatial pattern is recovered,[@balatsky] and one sees that the resonance in the large-gap regions is in fact hardly observable, particularly if one searches for such objects by looking for values of the 0 meV conductance which exceed the noise threshold, as in Ref. . Of course, applying the same filter mechanism to the Ni pattern will spoil the good agreement, so one is left with the unpleasant alternative of arguing that the effect of the intervening layers may be different in the case of the two impurities. This was in fact the conclusion reached by Ref. , but it destroys the utility of comparing the patterns for the two species as a way 