  Quark-lepton symmetry has been shown to be inconsistent with baryogenesis via
leptogenesis in natural schemes of the see-saw mechanism. Within the
phenomenological approach of textures, we relax this strict symmetry and
propose weaker conditions, namely models of the neutrino Dirac mass matrix
$M_D$ which have the same hierarchy as the matrix elements of $M_u$. We call
this guide-line generalized $hierarchical$ quark-lepton symmetry. We consider
in detail particular cases in which the moduli of the matrix elements of $M_D$
are equal to those of $M_u$. Within the phenomenological approach of textures,
we try for the heavy Majorana mass matrix diagonal and off-diagonal forms. We
find that an ansatz for $M_D$ preserving the hierarchy, together with an
off-diagonal model for the heavy Majorana neutrino mass, is consistent with
neutrino masses, neutrino mixing and baryogenesis via leptogenesis for an
intermediate mass scale $m_R \sim 10^{12}$ GeV. The preservation of the
hierarchical structure could come from a possible symmetry scheme.
