We compare an analytic model of jet quenching, based on the GLV non-Abelian energy loss formalism, to numerical results for the centrality dependent suppression of hadron cross sections in Au + Au and Cu + Cu collisions at RHIC. Simulations of neutral pion quenching versus the size of the colliding nuclear system are presented to high transverse momentum, . At low and moderate , we study the contribution of medium-induced gluon bremsstrahlung to single inclusive hadron production. In Pb + Pb collisions at the LHC, the redistribution of the lost energy is shown to play a critical role in yielding nuclear suppression that does not violate the participant scaling limit.