  In the framework of the two right-handed neutrino seesaw model, we consider
maximally-restrictive texture-zero patterns for the lepton Yukawa coupling and
mass matrices, together with the existence of a remnant CP symmetry. Under
these premisses, we find that several textures are compatible with the most
recent data coming from neutrino oscillation and neutrinoless double beta decay
experiments. It is shown that the number of allowed texture zeros depends on
the type of heavy right-handed neutrino mass spectrum. Namely, at most one
(two)-zero patterns are allowed in the Dirac Yukawa coupling matrix for
nondegenerate (degenerate) heavy Majorana neutrinos. The predictions for the
low-energy Dirac and Majorana CP-violating phases, and for the effective mass
parameter relevant in neutrinoless double-beta decay experiments, are presented
and discussed. We also comment on the impact of future experimental
improvements in scrutinising texture-zero patterns with a remnant CP symmetry,
within the minimal version of the seesaw mechanism considered here.
