It is widely believed among philosophers and educated people that it is virtuous to be open-minded. Instead of thinking of open-mindedness as universally or unconditionally epistemically valuable, I argue that it is vital to explicate the conditions that must obtain if open-mindedness is to be epistemically valuable. This paper critically evaluates open-mindedness given certain realistic cognitive limitations. I present and analyse a simple mathematical model of open-minded decision-making that incorporates these limitations. The results are mixed. The bad news is that (...) the circumstances where open-mindedness is epistemically valuable may be more restricted than previously thought especially if individuals are incapable of properly evaluating the trustworthiness of sources or the content of received information. The good news is that, if individuals are mildly competent in evaluating the trustworthiness of sources and the content of received information, then there are many circumstances where open-mindedness is epistemically valuable. (shrink)