Within the context of a Two Higgs Doublet Model supplemented by a discrete symmetry which treats each quark flavour differently, it is possible to provide a solution to the Strong CP problem: the strong CP phase is absent of the model at least until the two-loop level. In this model CP violation has an interesting origin: it arises due to a soft breaking (a dimension-two complex parameter in the scalar sector), but which preserves (at least to two loops) the CP properties of the scalars of the model. The model has tree-level flavour changing neutral currents, but enough freedom in the parameters of the model so that experimental constraints in the flavour and scalar sector can be fitted without fine tunings. The phenomenology of the model will be discussed, presenting the results of a fit to the parameter space and predictions for the properties of its heavier scalars.