In this paper, we present some new results on when extra risk strictly increases an option's value. We give a necessary and sufficient condition for a mean-preserving spread to strictly increase an option's value. We also give a necessary and sufficient condition for a risk change to strictly increase the values of options with strike prices in an open interval while preserving the values of all other options. These two results significantly improve the results given by Rasmusen (2007) (When does extra risk strictly increase an option's value? Review of Financial Studies, 20, 1647–1667).