  In this paper we analyze the compatibility of two-zero neutrino Majorana
textures with the recent experimental data. Differently from previous works, we
use the experimental data to fix the values of the non-vanishing mass matrix
entries and study in detail the correlations and degree of fine-tuning among
them, which is also a measure of how naturally a given texture is able to
describe all neutrino data. This information is then used to expand the
textures in powers of the Cabibbo angle; extracting random O(1) coefficients,
we show that only in few cases such textures reproduce the mixing parameters in
their 3 sigma ranges.
