  The related issues of Majorana CP violation in the lepton sector and
leptogenesis are investigated in detail in two rather generic supersymmetric
models with type I see-saw mechanism of neutrino mass generation and A_4
flavour symmetry, which naturally lead at leading order to tri-bimaximal
neutrino mixing. The neutrino sector in this class of models is described at
leading order by just two real parameters and one phase. This leads, in
particular, to significant low energy constraints on the Majorana phases
\alpha_{21} and \alpha_{31} in the PMNS matrix, which play the role of
leptogenesis CP violating parameters in the generation of the baryon asymmetry
of the Universe. We find that it is possible to generate the correct size and
sign of the baryon asymmetry in both A_4 models. The sign of the baryon
asymmetry is directly related to the signs of sin\alpha_{21} and/or
sin\alpha_{31}.
