We ask whether it is reasonable to delay or refuse to take COVID-19 vaccines that have been shown in clinical trials to be safe and effective against infectious diseases. We consider two kinds of vaccine hesitancy. The first is geared to scientifically informed open questions about vaccines. We argue that in cases where the data is not representative of relevant groups, such as pregnant women and ethnic minorities, hesitancy can be reasonable on epistemic grounds. However, we argue that hesitancy is (...) not reasonable if a vaccine has passed well-conducted clinical trials. The second kind of hesitancy is to do with beliefs about the institutions offering a successfully trialled vaccine and the justifiability of cooperating with those institutions. For example, in the UK, distrust of the UK Government or the National Health Service is identified as a factor in the vaccine hesitancy of minority ethnic populations. We ask whether this sort of hesitation is reasonable given normative requirements of fair co-operation, both with those institutions and the wider population. We suggest that the answer is not straightforward. Sometimes the hesitation is unreasonable but understandable. -/- . (shrink)