In bottom-up discovery proteomics, target-decoy competition (TDC) is the most popular method for false discovery rate (FDR) control. Despite unquestionable statistical foundations, this method has drawbacks, including its hitherto unknown intrinsic lack of stability vis-à-vis practical conditions of application. Although some consequences of this instability have already been empirically described, they may have been misinterpreted. This article provides evidence that TDC has become less reliable as the accuracy of modern mass spectrometers improved. We therefore propose to replace TDC by a totally different method to control the FDR at the spectrum, peptide, and protein levels, while benefiting from the theoretical guarantees of the Benjamini-Hochberg framework. As this method is simpler to use, faster to compute, and more stable than TDC, we argue that it is better adapted to the standardization and throughput constraints of current proteomic platforms.