Rising levels of external research funding represent not only an asset but also a challenge for universities. Academic leaders play a central role in managing the finances of their institutions, yet little is known about how they respond to the growing importance of external research funding. Through the lens of resource dependency theory, we argue that external funding can be seen as a critical resource for universities. In an interview-based study of academic leaders in Danish universities, we investigate how leaders respond to the uncertainties and constraints associated with their institutions' dependence on external funding. We find that increasing levels of external funding tie up a growing proportion of internal funding, constraining academic leaders' strategic options and challenging their ability to ensure continuity in research groups. Leaders respond by pursuing a variety of strategies, but many ultimately find themselves in a bind, caught between feeling a growing need to take actions to manage uncertainties and constraints resulting from rising levels of external funding on the one hand, and not wanting or daring to be seen as interfering with the autonomy of their high-performing researchers on the other. The risk, ultimately, is that external funding determines which research areas and talents are developed, and that all disposable internal funding in universities is tied up in externally funded activities.