Peptide identification is increasingly achieved through database searches in which mass precursor tolerance is set in the ppm range. This trend is driven by the high resolution and accuracy of modern mass spectrometers and the belief that the quality of peptide identification is fully controlled by estimating the false discovery rate (FDR) using the decoy-target approach. However, narrowing mass tolerance decreases the number of sequence candidates, and several authors have raised concerns that these search conditions can introduce inaccuracies. Here, we demonstrate that when scores that only depend on one sequence candidate are used, decoy-based estimates of the number of false positive identifications are accurate even with an average number of candidates of just 200, to the point that remarkably accurate FDR predictions can be made in completely different search conditions. However, when scores that are constructed taking information from additional sequence candidates are used together with low precursor mass tolerances, the proportion of peptides incorrectly identified may become significantly higher than the FDR estimated by the target-decoy approach. Our results suggest that with this kind of score the high mass accuracy of modern mass spectrometers should be exploited by using wide mass windows followed by postscoring mass filtering algorithms.