Lithium-oxygen cells, in which lithium peroxide forms in solution rather than on the electrode surface, can sustain relatively high cycling rates but require redox mediators to charge. The mediators are oxidised at the electrode surface and then oxidise lithium peroxide stored in the cathode. The kinetics of lithium peroxide oxidation has received almost no attention and yet is crucial for the operation of the lithium-oxygen cell. It is essential that the molecules oxidise lithium peroxide sufficiently rapidly to sustain fast charging. Here, we investigate the kinetics of lithium peroxide oxidation by several different classes of redox mediators. We show that the reaction is not a simple outer-sphere electron transfer and that the steric structure of the mediator molecule plays an important role. The fastest mediator studied could sustain a charging current of up to 1.9 A cm-2, based on a model for a porous electrode described here.