Recent research in quantitative theories for information-hiding topics, such as Anonymity and Secure Information Flow, tend to converge towards the idea of modeling the system as a noisy channel in the information-theoretic sense. The notion of information leakage, or vulnerability of the system, has been related in some approaches to the concept of mutual information of the channel. A recent work of Smith has shown, however, that if the attack consists in one single try, then the mutual information and other concepts based on Shannon entropy are not suitable, and he has proposed to use Rényi's min-entropy instead. In this paper, we consider and compare two different possibilities of defining the leakage, based on the Bayes risk, a concept related to Rényi min-entropy.