Drones will revolutionize 3D modeling. A 3D model represents an accurate reconstruction of an object or structure. This paper explores the design and implementation of ARES, which provides near real-time, accurate reconstruction of 3D models using a drone-mounted LiDAR; such a capability can be useful to document construction or check aircraft integrity between flights. Accurate reconstruction requires high drone positioning accuracy, and, because GPS can be in accurate, ARES uses SLAM. However, in doing so it must deal with several competing constraints: drone battery and compute resources, SLAM error accumulation, and LiDAR resolution. ARES uses careful trajectory design to find a sweet spot in this constraint space, a fast reconnaissance flight to narrow the search area for structures, and offloads expensive computations to the cloud by streaming compressed LiDAR data over LTE. ARES reconstructs large structures to within 10s of cms and incurs less than 100 ms compute latency.