In this article we describe another problem with journal impact factors by showing that one journal's impact factor is dependent on other journals' publication delays. The proposed theoretical model predicts a monotonically decreasing function of the impact factor as a function of publication delay, on condition that the citation curve of the journal is monotone increasing during the publication window used in the calculation of the journal impact factor; otherwise, this function has a reversed U shape. Our findings based on simulations are verified by examining three journals in the information sciences: the Journal of Informetrics, Scientometrics, and the Journal of the Association for Information Science and Technology.