Constraint Satisfaction and SAT can model planning problems and this approach is quite successful. There is an increasing interest in distributed and asynchronous search algorithms for solving distributed constraint satisfaction problems (DisCSP). An important motivation for distributed problem solving is the agents’ ability to keep their constraints private. Cryptographic techniques offer a certain protection from several types of attacks. However, when an attack succeeds, no agent can know how much privacy he has lost. We assume that agents enforce their privacy by dropping out of the search process whenever the estimated value of the information that they need to reveal in the future exceeds that attached to a successful solution of the DisCSP. We compare several distributed search algorithms as to how likely they are to terminate prematurely for privacy reasons, and arrange the algorithms in a hierarchy that reflects this relation.