Interpreting the potentially vast number of hypotheses generated by a shotgun proteomics experiment requires a valid and accurate procedure for assigning statistical confidence estimates to identified tandem mass spectra. Despite the crucial role such procedures play in most high-throughput proteomics experiments, the scientific literature has not reached a consensus about the best confidence estimation methodology. In this work, we evaluate, using theoretical and empirical analysis, four previously proposed protocols for estimating the false discovery rate (FDR) associated with a set of identified tandem mass spectra: two variants of the target-decoy competition protocol (TDC) of Elias and Gygi and two variants of the separate target-decoy search protocol of Käll et al. Our analysis reveals significant biases in the two separate target-decoy search protocols. Moreover, the one TDC protocol that provides an unbiased FDR estimate among the target PSMs does so at the cost of forfeiting a random subset of high-scoring spectrum identifications. We therefore propose the mix-max procedure to provide unbiased, accurate FDR estimates in the presence of well-calibrated scores. The method avoids biases associated with the two separate target-decoy search protocols and also avoids the propensity for target-decoy competition to discard a random subset of high-scoring target identifications.