A family of exactly self-gravitating, collisionless stellar systems with axial symmetry is presented. Each model exhibits quasi-Gaussian random motions that vary not at all with distance along any given ray from its center, and the circular speed in its equatorial plane is likewise independent of the radius. In essence, these models thicken the infinitesimally thin Zang disks to include the classical sec h-squared z plane-parallel solutions of Spitzer and Camm; the surprise here is that such alterations remain exact to arbitrary thicknesses. Two-component versions of these scale-free models yield some instructive disk-halo systems, including the ones proposed lately by Richstone and Miller. Their shapes and velocity fields are described in some detail.