Academic journals provide a key quality-control mechanism in science. Yet, information asymmetries and conflicts of interests incentivize scientists to deceive journals about the quality of their research. How can honesty be ensured, despite incentives for deception? I address this question by applying the theory of honest signaling to the publication process, using a simple model. This model reveals several mechanisms that can ensure honest journal submission, including differential benefits, differential costs, and costs to resubmitting rejected papers. Without submission costs, scientists benefit from submitting all papers to high-impact journals, unless papers can only be submitted a limited number of times. One implication of this analysis is that inefficiencies in academic publishing (e.g., arbitrary formatting requirements; long review times) can serve a function by disincentivizing scientists from submitting low-quality work to high-impact journals. This model generates a range of testable predictions and provides a tool for thinking about reforms to academic publishing.