Comparative genomics provides a general methodology for discovering functional DNA elements and understanding their evolution. The availability of many related genomes enables more powerful analyses, but requires rigorous phylogenetic methods to resolve orthologous genes and regions. Here, we use 12 recently sequenced Drosophila genomes and nine fungal genomes to address the problem of accurate gene-tree reconstruction across many complete genomes. We show that existing phylogenetic methods that treat each gene tree in isolation show large-scale inaccuracies, largely due to insufficient phylogenetic information in individual genes. However, we find that gene trees exhibit common properties that can be exploited for evolutionary studies and accurate phylogenetic reconstruction. Evolutionary rates can be decoupled into gene-specific and species-specific components, which can be learned across complete genomes. We develop a phylogenetic reconstruction methodology that exploits these properties and achieves significantly higher accuracy, addressing the species-level heterotachy and enabling studies of gene evolution in the context of species evolution.