  The generic predictions of two-texture zero neutrino mass matrices in the
flavor basis have been examined especially in relation to the degeneracies
between mass matrices within a class and interesting constraints on the
neutrino parameters have been obtained. It is shown that the knowledge of the
octant of $\theta_{23}$, the sign of $\cos\delta$ and neutrino mass hierarchy
can be used to lift these degeneracies.
