In recent years tax authorities worldwide have implemented voluntary disclosure schemes to recover tax on offshore investments. Such Schemes are characterized by the acquisition of non-audit information on offshore holdings, and a subsequent opportunity for affected taxpayers to make a voluntary disclosure. Accepted disclosures are subject to a discounted fine rate, but verified under-disclosure attracts a higher penalty. We characterize the optimal Scheme and show that an optimal Scheme can generate a Pareto improvement over the optimal auditing equilibrium without a Scheme, and can stimulate legitimate offshore investment activity. We show when a tax authority optimally gives incentives for honesty, and when it does not. The analysis yields practical design insights for policymakers.