It has been seen that inertial mismatches in 1D granular chains lead to remarkable energy absorption which increases with the number of spheres, N, and tapering, q. Short chains, however, are limited in that regard, and we therefore present one solution which greatly improves performance for any size chain. These strongly nonlinear and scalable systems feature surprisingly complicated dynamics and are inadequately represented by a hard-sphere approximation. Additionally, such systems have shock absorption capacities that vary as a function of position along the chain. In this Letter, we present results in the form of normalized kinetic energy diagrams to illustrate the impressive mitigation capability of both original and improved tapered chains. © 2006 The American Physical Society.