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Background: The increasing availability of sequence data for many viruses provides power to detect regions under unusual evolutionary constraint at a high resolution. One approach leverages the synonymous substitution rate as a signature to pinpoint genic regions encoding overlapping or embedded functional elements. Protein-coding regions in viral genomes often contain overlapping RNA structural elements, reading frames, regulatory elements, microRNAs, and packaging signals. Synonymous substitutions in these regions would be selectively disfavored and thus these regions are characterized by excess synonymous constraint. Codon choice can also modulate transcriptional efficiency, translational accuracy, and protein folding., Results: We developed a phylogenetic codon model-based framework, FRESCo, designed to find regions of excess synonymous constraint in short, deep alignments, such as individual viral genes across many sequenced isolates. We demonstrated the high specificity of our approach on simulated data and applied our framework to the protein-coding regions of approximately 30 distinct species of viruses with diverse genome architectures., Conclusions: FRESCo recovers known multifunctional regions in well-characterized viruses such as hepatitis B virus, poliovirus, and West Nile virus, often at a single-codon resolution, and predicts many novel functional elements overlapping viral genes, including in Lassa and Ebola viruses. In a number of viruses, the synonymously constrained regions that we identified also display conserved, stable predicted RNA structures, including putative novel elements in multiple viral species.