It is often suggested that the larger the size of risk, the larger our willingness to pay (WTP) for a given reduction of this risk. The authors show that this is not true in general in the expected utility model. The authors examine under which conditions the WTP for a marginal reduction in the size of risk is increasing. The authors also examine the closely related question of whether the risk premium is super-additive in the size of risk. Different necessary and/or sufficient conditions are provided when the different units of risks borne by the agent are either perfectly correlated or independent.