This paper proposes additional definitions of what it means for one decision maker to be more risk averse than another. These definitions build on the strongly more risk averse definition presented by Ross (Econometrica 49:621–663, 1981). Using examples from portfolio choice, self-protection and insurance demand, it is shown that these definitions of increased risk aversion facilitate clear-cut comparative statics analysis in decision models where traditional concepts of increased risk aversion are insufficient.