While gradient-index lenses are usually analyzed in terms of image fidelity, they are also capable of high flux concentration. In the first part of this presentation, the simplest class of gradient-index problems is revisited. An alterative way to obtain established solution of the refractive index profiles that produce perfect imaging is derived form the method of Fermat's strings and skewness conservation. The degree to which difference classes of such spherical lenses can realize the thermodynamic limit to flux concentration is explored. An answer is also sought to the intriguing question of the extent to which the spherical gradient-index lens of the fish eye is a modified Luneburg lens optimized subject to material constraints. The second half of this presentation addresses gradient-index rod lense. Both analytic methods and computer raytrace simulations are used for a comprehensive evaluation of their concentration and collection efficiency. They appear to be well suited as concentrators for the distal end of laser fiber-optic surgical units.