  We perform a systematic and complete analysis of texture zeros in the lepton
mass matrices and identify all viable and maximally restrictive cases of pairs
(M_\ell, M_D) and (M_\ell, M_L), where M_\ell, M_D and M_L are the
charged-lepton, Dirac neutrino and Majorana neutrino mass matrices,
respectively. To this end, we perform a thorough analysis of textures which are
equivalent through weak-basis permutations. Furthermore, we introduce numerical
measures for the predictivity of textures and apply them to the viable and
maximally restrictive texture zero models. It turns out that for Dirac
neutrinos these models can at most predict the smallest neutrino mass and the
CKM-type phase of the mixing matrix. For Majorana neutrinos most models can, in
addition, predict the effective neutrino mass for neutrinoless double beta
decay. Apart from one model, which has marginal predictive power with respect
to sin^2(theta_23), no other model can predict any of the already measured
observables.
