Longitudinal elastic impact between a hammer and an anvil is studied with regard to maximizing the peak value of the impact force. For a given hammer, an appropriately chosen elastic anvil can generate a "maximax" impact force which is greater than the corresponding value for a rigid anvil. The improvements can be up to 50% for a class of hammer-anvil combinations. Such optimum combinations are determined for long, cylindrical hammers and finite conical anvils.