High growth firms and reducing innovation barriers figure high in the European innovation policy debate. Do high growth firms face specific innovation barriers which are relevant for innovation policy? In this paper we study the robustness of the perception of innovation barriers when alternative definitions of high growth firms are used. Using data from two waves of the European Innovation survey (CIS 4 and CIS 2006) we show not only that different definitions of high growth firms lead to quite different results across country groups, but also that the results are quite different for the CIS 4 and CIS 2006 samples. We argue that in the light of the available empirical evidence this non-robustness should not come as a surprise and that this negative result makes it difficult to specifically target high growth firms with public policies. Fostering the emergence of high growth innovative firms in Europe may not be feasible with targeted funding policies only but needs a systemic approach.