  The application of Stein's method for distributional approximation often
involves so called Stein factors (also called 'magic factors') in the bound of
the solutions to Stein equations. However, in some cases these factors contain
additional (undesirable) logarithmic terms. It has been shown for many Stein
factors that the known bounds are sharp and thus that these additional
logarithmic terms cannot be avoided in general. However, no probabilistic
examples have appeared in the literature that would show that these terms in
the Stein factors are not just unavoidable artefacts, but that they are there
for a good reason. In this article we close this gap by constructing such
examples. This also leads to a new interpretation of the solutions to Stein
equations.
