We address the problem of enabling clients to regulate disclosure of their credentials and properties when interacting with servers in open scenarios. We provide a means for clients to specify the sensitivity of information in their portfolio at a fine-grain level and to determine the credentials and properties to disclose to satisfy a server request while minimizing the sensitivity of the information disclosed. Exploiting a graph modeling of the problem, we develop a heuristic approach for determining a disclosure minimizing released information, that offers execution times compatible with the requirements of interactive access to Web resources.