Effective Flavour Models do not address questions related to the nature of
the fundamental renormalisable theory at high energies. We study the
ultraviolet completion of Flavour Models, which in general has the advantage of
improving the predictivity of the effective models. In order to illustrate the
important features we provide minimal completions for two known A4 models. We
discuss the phenomenological implications of the explicit completions, such as
lepton flavour violating contributions that arise through the exchange of
messenger fields.Comment: 18 pages, 8 figure