Protocols for secure multiparty computation (SMC) allow a set of mutually distrusting parties to compute a function f of their private inputs while revealing nothing about their inputs beyond what is implied by the result. Depending on f, however, the result itself may reveal more information than parties are comfortable with. Almost all previous work on SMC treats f as given. Left unanswered is the question of how parties should decide whether it is "safe" for them to compute f in the first place. We propose here a way to apply belief tracking to SMC in order to address exactly this question. In our approach, each participating party is able to reason about the increase in knowledge that other parties could gain as a result of computing f, and may choose not to participate (or participate only partially) so as to restrict that gain in knowledge. We develop two techniques - -the belief set method and the SMC belief tracking method - -prove them sound, and discuss their precision/performance tradeoffs using a series of experiments. © 2012 ACM.