Experimental evidence for the existence of non-nuclear maxima in charg
e densities is questioned. It is shown that the non-nuclear maxima rep
orted for silicon are artifacts of the maximum entropy method that was
used to analyze the x-ray diffraction data. This method can be improv
ed by the use of appropriate prior information. We report systematic t
ests of the improved method leading to the absence of non-nuclear maxi
ma in Si. Likewise, the non-nuclear maxima reported earlier in berylli
um are not substantiated.