This paper explores the possibility that a taxation mechanism always implements a Pareto-optimal allocation in bilateral exchange when the market participants behave strategically and noncooperatively. To this end, we reconsider the taxation mechanism, namely the endowment taxation with transfers, implemented in the strategic bilateral exchange models by Gabszewicz and Grazzini (JPET, 1999). In this framework of strategic bilateral exchange, we consider a general class of smooth utility functions, and we determine the conditions under which the taxation mechanism is Pareto-optimal, i.e., whether there exists an equilibrium tax such that endowment taxation with transfers always implements a Pareto-optimal allocation. Furthermore, we explain why this taxation mechanism could implement a Pareto-optimal allocation.