Automated trust negotiation is the process of establishing trust between entities with no prior relationship through the iterative disclosure of digital credentials. One approach to negotiating trust is for the participants to exchange access control policies to inform each other of the requirements for establishing trust. When a policy is received at run-time, a compliance checker determines which credentials satisfy the policy so they can be disclosed. In situations where several sets of credentials satisfy a policy and some of the credentials are sensitive, a compliance checker that generates all the sets is necessary to insure that the negotiation succeeds whenever possible. Compliance checkers designed for trust management do not usually generate all the satisfying sets. In this paper, we present two practical algorithms for generating all satisfying sets given a compliance checker that generates only one set. The ability to generate all of the combinations provides greater flexibility in how the system or user establishes trust. For example, the least sensitive credential combination could be disclosed first. These ideas have been implemented in TrustBuilder, our prototype system for trust negotiation.