We present an approach to fusing hundreds of 3D point clouds to make complete models of 3D objects. The core motivating problem was how to manage registration error. For example, incremental image to image registration allows the registration errors to accumulate, and so the shape gradually distorts. The intuition was that one could create an alignment error minimization approach, whereby each individual scan minimized its registration error with all of the other scans. As each scan was attempting to do this independently, with the right registration error formulation, the scans would settle into a minimum error position. By alternating the update of view transforms and error estimation, the two solutions tend to mutually improve one another during the process and converge to appropriate solutions.