  We present a microscopic model for neutrino induced one-pion production off
the nucleon and its implementation for the purpose of calculating coherent pion
production in nuclei.
  We further criticize the use of the Rein--Sehgal model for coherent pion
production by low energy neutrinos. In particular, we show how the
approximations in that model give rise to a much flatter differential cross
section in the $\eta=E_\pi(1-\cos\theta_\pi)$ variable. We discuss the
limitations intrinsic to any approach based on the partial conservation of the
axial current hypothesis and the inability of such models to properly determine
the angular distribution of the outgoing pion with respect to the direction of
the incoming neutrino. We show the effects of those limitation for the case of
the $\frac{d\sigma}{d\eta}$ differential cross section.
