It has long been recognized that, in a restricted world of just two countries and two commodities, any feasible non-distorting international transfer can be replaced by a pair of individually distorting but collectively non-distorting equivalent import duties. In recent years it has sometimes been suggested that equivalence persists in broader contexts and there have been two attempts to provide interesting sufficient conditions for equivalence. Our purpose is three-fold. We first note that the sufficient conditions so far provided relate to the equilibrium values of endogenous variables (like prices) rather than to the given values of exogenous variables (like endowments, technologies and preferences) and that conditions of the former kind may be difficult to empirically justify. It is then shown, by means of a robust example with conditions imposed on exogenous variables only, that equivalence cannot be relied upon when there are more than two countries, even when the countries have no extraordinary features. Finally, we emphasize some of the difficulties in implementing equivalent tariffs even when they do exist.