Gradient-index (GRIN) lenses are predicted by many to have superior performance compared with lens systems using conventional homogeneous material compositions. Namely, the complexity of classic (i.e. homogeneous) multi-lens sequences required for high performance optical systems can be instead manifested into GRIN profile complexity, allowing for refraction throughout the volume of a lens and not just at the hard surface boundaries. As GRIN material technologies continue to evolve, facilitating more practical GRIN lens implementations, the knowledgebase and design tools to optimize GRIN lens systems must be simultaneously built. In this paper, one of the more unknown, yet crucially important, challenges of GRIN lens design is considered: dispersion. Dispersion and its effects on GRIN lenses are considered and a method to minimize its impact on the performance of GRIN lenses is outlined. Finally, a GRIN focusing lens based on the mixing of Germanium (Ge) and Silicon (Si) is proposed and designed to have minimal focal drift.