Using the fact that the neutrino mixing matrix
$U = U^\dagger_{e}U_{\nu}$, where $U_{e}$ and $U_{\nu}$
result from the diagonalisation of the charged lepton
and neutrino mass matrices, we analyse the sum rules which
the Dirac phase $\delta$ present in $U$
satisfies when $U_{\nu}$ has a form dictated by,
or associated with, discrete symmetries and
$U_e$ has a ``minimal'' form (in
terms of angles and phases it contains)
that can provide the requisite
corrections to $U_{\nu}$, so that
reactor, atmospheric and solar neutrino mixing angles
$\theta_{13}$, $\theta_{23}$ and $\theta_{12}$
have values compatible with the current data.
The following symmetry forms are considered:
i) tri-bimaximal (TBM), ii) bimaximal (BM)
(or corresponding to the conservation of the
lepton charge $L' = L_e - L_\mu - L_{\tau}$ (LC)),
iii) golden ratio type A (GRA),
iv) golden ratio type B (GRB),
and v) hexagonal (HG).
We investigate the predictions
for $\delta$ in the cases of
TBM, BM (LC), GRA, GRB and HG forms
using the exact and the leading order sum rules
for $\cos\delta$ proposed in the literature,
taking into account also the uncertainties
in the measured values of
$\sin^2\theta_{12}$, $\sin^2\theta_{23}$ and $\sin^2\theta_{13}$.
This allows us, in particular, to assess
the accuracy of the predictions for $\cos\delta$
based on the leading order sum rules and
its dependence on the values
of the indicated neutrino mixing parameters
when the latter are varied in their respective
3$\sigma$ experimentally allowed ranges.
