We consider a principal-agent setting with two types of risk averse agents with different abilities to avoid losses. Abilities (types) are characterized by two distributions F and G which are agents' private information. All agents have the same increasing and strictly concave utility function U, under which G has a higher certainty equivalent. In this environment we derive a characterization of pairs of distributions under which a first best outcome can be achieved or approximated. We prove that a first best outcome can be achieved if and only if the distribution F is not absolutely continuous with respect to the distribution G. If this condition is not satisfied, the first best outcome can be approximated (arbitrarily close) if and only if the likelihood ratio dF/dG is unbounded. Journal of Economic Literature Classification Number: D82.