  We examine the possibility that a certain class of neutrino mass matrices,
namely those with two independent vanishing minors in the flavor basis,
regardless of being invertible or not, is sufficient to describe current data.
We compute generic formulae for the ratios of the neutrino masses and for the
Majorana phases. We find that seven textures with two vanishing minors can
accommodate the experimental data. We present an estimate of the mass matrix
for these patterns. All the possible textures can be dynamically generated
through the seesaw mechanism augmented with a discrete Abelian symmetry.
