This paper assesses whether the allocation puzzle - the tendency for capital to flow to countries with relatively low productivity growth - is observed for foreign direct investment (FDI) flows, which should be particularly sensitive to productivity prospects. We look both at aggregate FDI flows and, using a new data set, at FDI flows into the main economic sectors. We make three points. First, we do not find evidence of an allocation puzzle for aggregate FDI flows. Second, we refine the aggregate result and document substantial sectoral heterogeneity. An allocation puzzle is observed in the agriculture, construction, mining/petroleum/utilities and tourism sector. By contrast, we show that countries with faster productivity growth in manufacturing attract more investment in that sector. The link is even stronger for service sectors. Third, we document a role for financial openness: a country with fast productivity growth draws in more FDI into its service sectors only when it is financially open. We conclude with a discussion of some tentative explanations for the results.