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Using a new set of measures of concentration of trade, I suggest that the opening up of trade to date has been greatly exaggerated. At least judging on the basis of trade concentration, agriculture and service sectors should barely be seen as globalised at all. Contrary to other recent studies, Europe's main economies lag behind the USA in terms of global openness, and most are behind Japan, Canada and China. The Balkans, Poland and Czech Republic are near the bottom end of the global openness league table. Since there is a strong correlation between concentration of trade and poor economic performance, this should be of concern to those countries and to the European Union.