It is shown that the Brillouin zone integral for the interstitial KKR
Green function can be evaluated accurately by taking proper care of th
e free-electron singularities in the integrand. The proposed method co
mbines two recently developed methods, a supermatrix method and a subt
raction method. This combination appears to provide a major improvemen
t compared with an earlier proposal based on the subtraction method on
ly. Consequently, the barrier preventing the study of important inters
titial-like defects, such as an electromigrating atom halfway along it
s jump path, can be considered as being razed.