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

Hierarchical pinning model: low disorder relevance in the $b=s$ case