Complex trade policies, mixing different tools applied at heterogeneous level on specific products, are not compatible with abrupt quantitative economic models. The present paper proposes a pragmatic modelling solution for solving this issue. It allows to use the most disaggregated information available i.e. trade and protection data in a standard framework, here the GTAP model and database. On the theoretical aspect, we open the black box of the standard Armington approach applied in an aggregated framework. We separate the bundle effect of an aggregated trade flow composed of different specific products (such as different HS6 lines), and the real geographical specificities of varieties. Moreover, we look at the issue of zero-trade flows that are usually badly treated in CGE models. Using GTAPAgr model, we apply our disaggregation strategy to the dairy sector with a simple and illustrative case with two sub-products. The role of taking into account heterogeneous structure of trade and protection and the possibility of exclusion of some producers, i.e. trade flows going to zero, is demonstrated.