In McLean and Postlewaite (2001), we analyzed a general equilibrium model with asymmetrically informed agents. We presented a notion of informational size and showed (among other things) that when agents' information as a whole resolved nearly all the uncertainty, the conflict between incentive compatibility and (ex post) efficiency can be made arbitrarily small if agents are sufficiently small informationally. This paper extends the analysis of the relationship between informational size and efficiency to the case in which there is nontrivial aggregate uncertainty, that is, when there is significant uncertainty about the world even when the information of all agents is known. We further show that the conflict between incentive compatibility and efficiency asymptotically vanishes when an economy is replicated.