In distributed work systems, individual users perform work for other users. A significant challenge in these systems is to provide proper incentives for users to contribute as much work as they consume, even when monitoring is not possible. We formalize the problem of designing "incentive-compatible accounting mechanisms" that measure the net contributions of users, despite relying on voluntary reports. We introduce the Drop-Edge Mechanism that removes any incentive for a user to manipulate via misreports about work contributed or consumed. We prove that Drop-Edge provides a good approximation to a user's net contribution, and is accurate in the limit as the number of users grows. We demonstrate very good welfare properties in simulation compared to an existing, manipulable mechanism. In closing, we show the power of sybil attacks in accounting mechanisms and discuss our ongoing work, including a real-world implementation and evaluation of the Drop-Edge Mechanism in a BitTorrent client.