Audit cut-off rules are policy tools widely adopted by fiscal authorities with the aim to improve voluntary tax compliance. Despite their usefulness, audits are costly for the fiscal authority, so determining how best to allocate controls is a key policy issue. In the audit framework presumptive taxation could be used to identify the cut-off rule, allowing fiscal authorities to uncover firms’ under-reporting. However, an audit rule based on presumptions does not allow distinguishing whether the presence of under-reporting is due to voluntary non-compliance or to a lack of managerial skills. Therefore, this paper proposes to combine an audit rule based on a presumptive cut-off with a measure of efficiency, with the aim to solve the main weakness of the presumptive methods. In particular, we develop an integrated approach that is able to support the audit activities of fiscal authorities. For illustrative purposes we support our approach with an empirical application based on a sample of Italian firms.