  We investigate, within the Type I seesaw framework, the physical implications
of zero textures in the Yukawa couplings which generate the neutrino Dirac mass
matrix $m_D$. It is shown that four is the maximal number of texture zeroes
compatible with the observed leptonic mixing and the assumption that no
neutrino mass vanishes. We classify all allowed four-zero textures of $m_D$
into two categories with three classes each. We show that the different
classes, in general, admit CP violation both at low and high energies. We
further present the constraints obtained for low energy physics in each case.
The r\^ ole of these zero textures in establishing a connection between
leptogenesis and low energy data is analysed in detail. It is shown that it is
possible in all cases to completely specify the parameters relevant for
leptogenesis in terms of light neutrino masses and leptonic mixing together
with the unknown heavy neutrino masses.
