Political actors face a trade-off when they try to influence the beliefs of voters about the effects of policy proposals. They want to sway voters maximally, yet voters may discount predictions that are inconsistent with what they already hold to be true. Should political actors moderate or exaggerate their predictions to maximize persuasion? I extend the Bayesian learning model to account for confirmation bias and show that only under strong confirmation bias are predictions far from the priors of voters self-defeating. I use a preregistered survey experiment to determine whether and how voters discount predictions conditional on the distance between their prior beliefs and the predictions. I find that voters assess predictions far from their prior beliefs as less credible and, consequently, update less. The paper has important implications for strategic communication by showing theoretically and empirically that the prior beliefs of voters constrain political actors.