What do attacks on 'unpalatable' research reveal about academic freedom? When academic work is curtailed, this cherished yet misunderstood concept is undermined. Silencing based on moral objection -- rather than wrongdoing -- suggests academic freedom is more constrained than we believe. On paper, academic freedom is rule-bound, yet 'dangerous' ideas produce overwhelmingly visceral reactions. It was these emotional responses I examined to explore the difference between what we believe academic freedom to be, and how it manifests in contentious fields. I conducted qualitative interviews with 18 researchers whose work elicited condemnation or constraint beyond 'legitimate' scholarly critique. I used mixed-methods data analysis to determine shared themes and characteristics. While academic institutions uphold their commitment to unfettered enquiry, 'academic freedom' is highly contingent and subject to the values of players in a range of disciplinary and institutional fields that together yield a generalised field of 'academic research'. This research challenges assumptions about 'freedom' by identifying parameters that bound the notion. I argue the concept is indeed bounded, and that academics become aware of those bounds when they bump up -- often unexpectedly -- against them.