In this paper we investigate the effectiveness and the welfare implications of various fiscal policies in strategic bilateral trade. To this end, we reconsider the class of bilateral oligopoly models with taxation implemented in Gabszewicz and Grazzini (1999, 2001). Assuming the preferences of traders are represented by CES utility functions with non unitary shares on consumption, we determine the Cournot-Nash equilibria, and we study the effects of two fiscal policies with transfers. We show that both fiscal policies with transfers implement a first-best allocation only when commodities are perfect complements or perfect substitutes.