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This paper analyses a process where a catching-up economy, Estonia, has been designing the governance of the science and innovation system in the context of the institutional restructuring of Eastern Europe since the 1990s, influenced by international policy convergence in Europe and the US towards an optimal governance system. This is based on a move from the "public good" to the "network" rationale and a policy emphasis on increasing the direct and short-term societal relevance of science and innovation systems. The paper analyses the levels of convergence vs. divergence of the Estonian governance system and argues that the over-emphasis on policy features in the international policy debates has brought about an under-emphasis on crucial structural features of the governance system. The paper concludes that there are different levels of convergence and divergence that matter, and the Estonian science and innovation system faces both policy and also even more important structural challenges in making the governance system more responsive to socio-economic needs.