  We discuss the question why the mixing $U_{e3}$ is small. The natural answer
is $U_{e3}=0$ in some symmetric limit, in which two large mixings are realized.
It is possible to force $U_{e3}$ and $\cos{2 \theta_{23}}$ to be zero by
imposing a discrete symmetry. We investigate a special class of symmetries
$Z_2$ and of the consequences of their perturbative violation.
