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We introduce a very fundamental and important axiom of the non-dummy. This states that each agent can change the outcome of the mechanism at some preference profile, thus guaranteeing every agent the minimum right to affect the social decision. We study the possibility of strategy-proof, efficient and non-dummy mechanisms in pure exchange economies. We provide two new interesting classes of such mechanisms. The results shed light on the structure of strategy-proof and efficient mechanisms, and should promote a complete characterization of those mechanisms in pure exchange economies with three or more agents.