Constraint satisfaction has been a very successful paradigm for solving problems such as resource allocation and planning. Many of these problems pose themselves in a context involving multiple agents, and protecting privacy of information among them is often desirable. Secure multiparty computation (SMC) provides methods that in principle allow such computation without leaking any information. However, it does not consider the issue of keeping agents' decisions private from one another. In this paper, we show an algorithm that uses SMC in distributed computation to satisfy this objective.