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.
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