We analyze the mechanism-design problem of a principal allocating amounts of a perfectly divisible good to n agents, each of whom desires as much of the good as possible. The principal has an ideal allocation for each agent, which is private information held by that agent. The principal has access to an auditing technology that allows her to perfectly uncover the private information of any k (< n) of the agents. We present a tractable approach to solve for the principal’s optimal mechanism, which combines targeted random audits with allocative distortions to ensure compliance. Agents whose reported type falls above a cutoff enter a pool for random audits. The allocation to audited agents coincides with the principal’s ideal. For unaudited agents, upward distortions reward conservative reporting, while downward distortions discipline over-reporting.