This paper develops a simple model to explore whether a higher detection probability for offshore tax evaders—e.g. because of improved exchange of information between countries and/or due to digitalization of tax administrations—renders it optimal for governments to introduce a voluntary disclosure program (VDP) and, if so, under what terms. We find that if the VDP is unanticipated, it is likely to be optimal for a revenue-maximizing government to introduce a VDP with relatively generous terms, i.e. a low or even negative penalty. When anticipated, however, the VDP is neither incentive compatible nor optimal, as it induces otherwise compliant taxpayers to evade tax. A VDP can then only be beneficial if tax evasion induces an external social cost beyond the direct revenue foregone, e.g., due to adverse effects on overall tax morale. In contrast to the common view that VDPs should come along with additional enforcement effort, we find that governments should relax enforcement if the VDP itself provides more powerful incentives to come clean.