Inferring the intensity of positive selection in protein-coding genes is important since it is used to shed light on the process of adaptation. Recently, it has been reported that overlapping genes, which are ubiquitous in all domains of life, seem to exhibit inordinate degrees of positive selection. Here, we present a new method for the simultaneous estimation of selection intensities in overlapping genes. We show that the appearance of positive selection is caused by assuming that selection operates independently on each gene in an overlapping pair, thereby ignoring the unique evolutionary constraints on overlapping coding regions. Our method uses an exact evolutionary model, thereby voiding the need for approximation or intensive computation. We test the method by simulating the evolution of overlapping genes of different types as well as under diverse evolutionary scenarios. Our results indicate that the independent estimation approach leads to the false appearance of positive selection even though the gene is in reality subject to negative selection. Finally, we use our method to estimate selection in two influenza A genes for which positive selection was previously inferred. We find no evidence for positive selection in both cases.