In the last chapter a new Finite-Volume scheme was specifically constructed to dissipate as much entropy as admissible. The admissible amount of dissipation was bound using error estimates for the recovery of point values. This chapter starts from the same point, but concentrates on Discontinuous Galerkin schemes. We will correct these schemes to dissipate an amount of entropy that is, under mild assumptions, higher than the amount dissipated by any exact solution.