We propose a novel approach to buildinginfluence-driven ex-planations(IDXs) for (discrete) Bayesian network classifiers (BCs). IDXsfeature two main advantages wrt other commonly adopted explanationmethods. First, IDXs may be generated using the (causal) influences between intermediate, in addition to merely input and output, variables within BCs, thus providing adeep, rather than shallow, account of theBCs’ behaviour. Second, IDXs are generated according to a configurable set of properties, specifying which influences between variables count to-wards explanations. Our approach is thusflexible and can be tailored to the requirements of particular contexts or users. Leveraging on this flexibility, we propose novel IDX instances as well as IDX instances cap-turing existing approaches. We demonstrate IDXs’ capability to explainvarious forms of BCs, and assess the advantages of our proposed IDX instances with both theoretical and empirical analyses.