  The generic predictions of inverse Majorana neutrino mass matrix,
$M_{\nu}^{-1}$ with texture two zeros, in the basis where charged lepton mass
matrix is diagonal, have been obtained for neutrino masses and mixings,
especially, $\theta_{13}$ and CP-violating phases. Such type of mass models are
natural in the context of seesaw models with Dirac neutrino mass matrix,
$M_{D}$, diagonal. Out of the fifteen possible texture two zeros patterns of
the inverse neutrino mass matrix only seven are found to be compatible with the
available data on neutrino masses and mixings including the latest $T\emph{2}K$
observation of non-zero $\theta_{13}$. It is, also, found that $\theta_{13}=0$
is disallowed in the mass models investigated in the present work. While the
neutrino mass matrices of type I and II are found to be necessarily CP
violating, type III is found to be CP-violating for a special case where
$\theta_{23}$ lie above maximality. The atmospheric mixing angle, $\theta_{23}$
is found to dictate the possible hierarchies in type I and II neutrino mass
models. For type III, additional information regarding $m_{ee}$ will be
required to rule out the inverted hierarchy (IH). A maximal $\theta_{23}$ is
found to be disallowed in all types of texture two zero $M_{\nu}^{-1}$
Ans$\ddot{a}$tz.
