The purpose of this paper is to establish a new upper bound on the size of the strategy space that is needed to feasibly implement the constrained Walrasian correspondence (W). This bound is significantly lower than those available from the literature on feasible Nash-implementation. Our focus on W has wider implications since implementation of W implies partial implementation of "almost" all individually rational and efficient implementable economic performance standards. Hence, our results provide a parallel - in the economic context - to the research agenda of Saijo [13] and McKelvey [9] who have established new upper bounds on the size of the strategy space required for feasible implementation of Nash-implementable performance standards in general social choice contexts. We prove that it is sufficient to have only three agents in an economy who make price-related announcements. This is a critical source of the reduction in strategy space. © 1991 Spring-Verlag.