  We present an $A4$-based model where neutrino masses arise from a combination
of see-saw mechanisms. The model is motivated by several small mixing and mass
parameters indicated by the data. These are $\theta_{13}$, the solar mass
splitting, and the small deviation of $\theta_{23}$ from maximal mixing (=
$\pi/4$). We take the above as indications that at some level the small
quantities are well-approximated by zero. In particular the mixing angles, to a
zero order, should be either 0 or $\pi/4$. Accordingly, in this model the
Type-II see-saw dominates and generates the larger atmospheric mass splitting
and sets $\theta_{23} = \pi/4$. The other mixing angles are vanishing as is the
solar splitting. We show how the $A4$ assignment for the lepton doublets leads
to this form. We also specify the $A4$ properties of the right-handed neutrinos
which result in a smaller Type-I see-saw contribution that acts as a
perturbation and shifts the angles $\theta_{12}$ and $\theta_{13}$ into the
correct range and the desired value of $\Delta m^2_{solar}$ is produced. The
$A4$ symmetry results in relationships between these quantities as well as with
a small deviation of $\theta_{23}$ from $\pi/4$. If the right-handed neutrino
mass matrix, $M_R$, is chosen real then there is no leptonic CP-violation and
only Normal Ordering is admissible. If $M_R$ is complex then Inverted Ordering
is also allowed with the proviso that the CP-phase, $\delta$, is large, i.e.,
$\sim \pi/2$ or $-\pi/2$. The preliminary results from NO$\nu$A favouring
Normal Ordering and $\delta$ near $-\pi/2$ imply quasi-degenerate neutrino
masses in this model.
