The National Institute of Standards and Technology is involved in developing standard protocols for the performance evaluation of 3D imaging systems, which include laser scanners and LADARs (LAser Detection and Ranging). A LADAR is an optical device that typically yields voluminous 3D "point clouds" by scanning scenes. In many applications, a model of an object which is present in the scene has been specified, and the task amounts to recovering this object from scan data. Specifically, the recovery of spheres from point clouds will be addressed, aiming at estimating the location of their centers and, if not known beforehand, their radii. This information can be used, for instance, to "register" LADAR data to a specified coordinate frame. Two experiments recovering spheres based on best-fitting data points are reported. Sphere fitting based on orthogonal least squares is compared to a novel approach, minimizing instead the squares of range errors incurred in the direction of the scan.