  The searches for an underlying pattern in neutrino masses have motivated
different proposals for textures in the neutrino mass matrix, which is also
related to particular arranges of the mixing matrix. The current precise
determinations of neutrino mixings have discarded some of the most studied
proposals, such as the one involving a $\mu-\tau$ exchange symmetry. In this
work, we investigate the relation of a still allowed $\mu-\tau$ reflection
symmetry with the constraints of a magic pattern in the neutrino mass matrix.
We show that both conditions cannot be fulfilled simultaneously in an exact but
rather in an approximate way. Such considerations are used to restrict the
values of CP-violating phases and some observables, like the neutrinoless
double beta decay amplitude and the solar angle, that can be explored with
forthcoming results.
