  We consider the type I see-saw model with two right-handed neutrinos and a
normal neutrino mass hierarchy and impose a zero coupling between the
right-handed neutrino mainly responsible for the atmospheric neutrino mass and
the electron neutrino. We derive a master formula which relates see-saw input
parameters in a one to one correspondence with physical neutrino observables.
Using the master formula we search for simple ratios of couplings consistent
with current data on neutrino mass and lepton mixing. We discover a minimal
predictive example in which the right-handed neutrino mainly responsible for
the atmospheric neutrino mass has couplings to (nu_e, nu_mu, nu_tau)
proportional to (0,1,1) and the right-handed neutrino mainly responsible for
the solar neutrino mass has couplings to (nu_e, nu_mu, nu_tau) proportional to
(1,1,3) or (1,3,1), with a relative phase eta = -/+ pi/3, providing the link
between leptogenesis and CP violation in neutrino oscillation experiments. We
show how these patterns of couplings could arise from an A_4 family symmetry
model of leptons which predicts all the PMNS parameters in terms of the
neutrino mass ratio m_2/m_3, corresponding to approximate Tri-bimaximal-Cabibbo
mixing, accurate to one degree, with the prediction delta = +/- pi/2.
