We initiate an investigation of general fault-tolerant distributed computation in the full-information model. In the full information model no restrictions are made on the computational power of the faulty parties or the information available to them. (Namely, the faulty players may be infinitely powerful and there are no private channels connecting pairs of honest players). Previous work in this model has concentrated on the particular problem of simulating a single bounded-bias global coin flip (e.g., Ben-Or and Linial [Randomness and Computation, S. Micali, ed., JAI Press, Greenwich, CT, 1989, pp. 91–115] and Alon and Naor [SIAM J. Comput., 22 (1993), pp. 403–417]). We widen the scope of investigation to the general question of how well arbitrary faulttolerant computations can be performed in this model. The results we obtain should be considered as first steps in this direction. We present efficient two-party protocols for fault-tolerant computation of any bivariate function...