In a recent article in the British Journal for the Philosophy of Science, Heesen and Bright argue that prepublication peer review should be abolished and replaced with postpublication peer review (provided the matter is judged purely on epistemic grounds). In this article, I show that there are three problems with their argument. First, it fails to consider the epistemic cost of implementing the change to postpublication peer review. Second, it fails to consider some potential epistemic benefits of prepublication peer review, which involve avoiding bias. Third, it fails to consider some potential epistemic disadvantages of postpublication peer review, which stem from the greater number of papers that would be published under that system.