  We study the consequences of the $Z_2$-symmetry behind the $\mu$--$\tau$
universality in neutrino mass matrix. We then implement this symmetry in the
type-I seesaw mechanism and show how it can accommodate all sorts of lepton
mass hierarchies and generate enough lepton asymmetry to interpret the observed
baryon asymmetry in the universe. We also show how a specific form of a
high-scale perturbation is kept when translated via the seesaw into the low
scale domain, where it can accommodate the neutrino mixing data. We finally
present a realization of the high scale perturbed texture through addition of
matter and extra exact symmetries.
