Hybrid modelling approaches are increasingly used to bridge the historical gap between the bottom-up (BU) and top-down (TD) approaches to energy/economy/environment (E3) modelling. By nature, they require a substantial effort of harmonisation between national accounts and energy balance data. For most computable general equilibrium (CGE) models defined at the scale of a given country, efforts have been made to reconcile those data. But the methods being used and their impacts on the empirical information are generally poorly documented. Models domains corresponding to multiple countries rely on hybrid datasets whose characteristics and methods of production are not explored in details. Such an exploration is required, however, because different hybridisation techniques have different impacts on key empirical features that are important for policy evaluation. After reviewing the literature on hybridisation methods, this paper proposes an innovative procedure for building hybrid Input-Output matrices at the scale of a country, and illustrates it with data for France. Compared to existing methods, this procedure includes information about energy flows, prices and quantities coming from energy statistics, without alteration on this data. All this information is then introduce within a consistent social accounting framework. The impact of this method is illustrated in a standard Capital-Labour-Energy (‘KLEM’) CGE model. The welfare costs of the same price-induced energy policy are evaluated, keeping the same behavioural structural assumptions and parameters. The model is alternatively calibrated either using our hybrid matrices or unmodified original input-output data from national accounts. This comparison shows that the model calibrated on hybridised data produce systematically lower welfare costs estimates, when targeting energy reduction alternatively on firm consumptions and household consumptions.