  We update and improve past efforts to predict the leptonic Dirac CP-violating
phase with models that predict perturbatively modified tribimaximal or
bimaximal mixing. Simple perturbations are applied to both mixing patterns in
the form of rotations between two sectors. By translating these perturbed
mixing matrices to the standard parameterization for the neutrino mixing matrix
we derive relations between the Dirac CP-phase and the oscillation angles. We
use these relations together with current experimental results to constrain the
allowed range for the CP-phase and determine its probability density.
Furthermore, we elaborate on the prospects for future experiments probing on
the perturbations considered in this work. We present a model with $A_4$
modular symmetry that is consistent with one of the described perturbed
scenarios and successfully predicts current oscillation parameter data.
