The historical signal in nucleotide sequences becomes eroded over time by substitutions occurring repeatedly at the same sites. This phenomenon, known as substitution saturation, is recognized as one of the primary obstacles to deep-time phylogenetic inference using genome-scale data sets. We present a new test of substitution saturation and demonstrate its performance in simulated and empirical data. For some of the 36 empirical phylogenomic data sets that we examined, we detect substitution saturation in around 50% of loci. We found that saturation tends to be flagged as problematic in loci with highly discordant phylogenetic signals across sites. Within each data set, the loci with smaller numbers of informative sites are more likely to be flagged as containing problematic levels of saturation. The entropy saturation test proposed here is sensitive to high evolutionary rates relative to the evolutionary timeframe, while also being sensitive to several factors known to mislead phylogenetic inference, including short internal branches relative to external branches, short nucleotide sequences, and tree imbalance. Our study demonstrates that excluding loci with substitution saturation can be an effective means of mitigating the negative impact of multiple substitutions on phylogenetic inferences. [Phylogenetic model performance; phylogenomics; substitution model; substitution saturation; test statistics.].