  We propose a class of Two Higgs Doublet Models where there are Flavour
Changing Neutral Currents (FCNC) at tree level, but under control due to the
introduction of a discrete symmetry in the full Lagrangian. It is shown that in
this class of models, one can have simultaneously FCNC in the up and down
sectors, in contrast to the situation encountered in BGL models. The intensity
of FCNC is analysed and it is shown that in this class of models one can
respect all the strong constraints from experiment without unnatural
fine-tuning. It is pointed out that the additional sources of flavour and CP
violation are such that they can enhance significantly the generation of the
Baryon Asymmetry of the Universe, with respect to the Standard Model.
