Over-precision is the most robust and least understood form of overconfidence. In an attempt to elucidate the underlying causes of over-precision in judgment, the present paper offers a new approach — examining people’s beliefs about the likelihood of chance events drawn from known probability distributions. This approach allows us to test the assumption that low hit rates inside subjective confidence intervals arise because those confidence intervals are drawn too narrowly. In fact, subjective probability distributions are systematically too wide, or insufficiently precise. This result raises profound questions for the study of overconfidence.