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Predictions about the effects of climate change cannot be made with complete certainty, so acknowledging uncertainty may increase trust in scientists and public acceptance of their messages. Here we show that this is true regarding expressions of uncertainty, unless they are also accompanied by acknowledgements of irreducible uncertainty. A representative national sample of Americans read predictions about effects of global warming on sea level that included either a worst-case scenario (high partially bounded uncertainty) or the best and worst cases (fully bounded uncertainty). Compared to a control condition, expressing fully bounded but not high partially bounded uncertainty increased trust in scientists and message acceptance. However, these effects were eliminated when fully bounded uncertainty was accompanied by an acknowledgement that the full effects of sea-level rise cannot be quantified because of unpredictable storm surges. Thus, expressions of fully bounded uncertainty alone may enhance confidence in scientists and their assertions but not when the full extent of inevitable uncertainty is acknowledged.