This paper analytically derives the conditions under which the slope of the tax reaction function is negative in a classical tax competition model. If countries maximize welfare, we show that a negative slope (reflecting strategic substitutability) occurs under relatively mild conditions. Simulations suggest that strategic substitutability occurs under plausible parameter configurations. The strategic tax response is crucial for understanding tax competition games, as well as for assessing the welfare effects of partial tax unions (whereby a subset of countries coordinate their tax rates). Indeed, contrary to earlier findings that have assumed strategic complementarity in tax rates, we show that partial tax unions might reduce welfare under strategic substitutability.