  We analyze the arguments put forward recently by Niedermayer et al in favor
of the correctness of conventional perturbation theory in non-Abelian models
and supposedly showing that our super-instanton counterexample was sick. We
point out that within their own set of assumptions, the proof of Niedermayer et
al regarding the correctness of perturbation theory is incorrect and provide a
correct proof under more restrictive assumptions. We reply also to their claim
that the S-matrix bootstrap approach of Balog et al supports the existence of
asymptotic freedom in the O(3) model.
