The credibility of think tanks is grounded in their image as independent experts. In order to gain authority to act, think tanks must be seen as independent, but in order to exert influence and gain funding, think tanks are forced to compromise this independent image. We focus on how think tanks handle this independence paradox. How do think tanks use different resources to construct an independent image? The aim of the article is conceptual, as we develop a theoretical model of the independence paradox. This conceptual work is based on empirical analysis of attempts by think tanks in Poland and Sweden to create independence while maintaining influence. The two desirables central for think tanks, independence and influence, force them to make strategic choices about their relations with various actors. We conclude that the processes of keeping distance and arranging proximity are at the core of the independence paradox. © 2020 The Authors. Governance published by Wiley Periodicals LLC.