This paper consideres the problem of designing "better" mechanisms whose Nash allocations coincide with constrained Walrasian allocations for nonneoclassical economies under the minimal possible assumptions. We show that no assumprions on preferences are needed for feasible and continuous implementation of the constrained Walrasian correspondence. Further, under the monotonicity assumption, we present a mechanism that is completely feasible and continuous. Hence, no continuity and convexity assumptions on preferences are required, and preferences may be nontotal or nontransitive. Thus, this paper gives a somewhat positive answer to the question raised in the literature by showing that, even for non-neoclassical economies, there are "incentive-compatible", "privacy preserving", and "well-behaved" mechanisms which yield Pareto-efficient and individually rational allocations at Nash equilibria. * I wish to thank J. S. Chipman, J. Jordan, M. Richter, H. Weinberger, the editor, and two anonymous referees for useful comments and suggestions. I am particularly thankful to L. Hurwicz who stimulated my interest in this problem and provided detailed comments and suggestions.