It is known that with incomplete information, there are Bayesian mechanisms that undertake public projects achieving ex post efficiency and budget balance. However, there are two shortcomings in these mechanisms. First, the mechanism designer is required to know the agents' prior beliefs, which is quite demanding. Second, the mechanism may possess multiple equilibria including undesirable ones. This paper presents a Bayesian mechanism that is nonparametric in that the mechanism designer cannot incorporate any:information other than that received from the agents. Moreover, at all undominated Bayesian equilibria of the mechanism, the public project is undertaken efficiently and budget is balanced. Journal of Economic Literature Classification Numbers: C72, D78, D82. (C) 1999 Academic Press.