  We discuss the viability of the $\mu$--$\tau$ interchange symmetry imposed on
the neutrino mass matrix in the flavor space. Whereas the exact symmetry is
shown to lead to textures of completely degenerate spectrum which is
incompatible with the neutrino oscillation data, introducing small
perturbations into the preceding textures, inserted in a minimal way, lead
however to four deformed textures representing an approximate $\mu$--$\tau$
symmetry. We motivate the form of these `minimal' textures, which disentangle
the effects of the perturbations, and present some concrete realizations
assuming exact $\mu$--$\tau$ at the Lagrangian level but at the expense of
adding new symmetries and matter fields.
  We find that all these deformed textures are capable to accommodate the
experimental data, and in all types of neutrino mass hierarchies, in particular
the non-vanishing value for the smallest mixing angle.
