  We consider a hierarchical pinning model introduced by B.Derrida, V.Hakim and
J.Vannimenus which undergoes a localization/delocalization phase transition.
This model depends on two parameters $b$ and $s$. We show that in the
particular case where $b=s$, the disorder is weakly relevant, in the sense that
at any given temperature, the quenched and the annealed critical points
coincide. This is in contrast with the case where $b \neq s$.
