A central goal in genome biology is to understand the origin and maintenance of genic diversity. Over evolutionary time, each gene's contribution to the genic content of an organism depends not only on its probability of long-term survival, but also on its propensity to generate duplicates that are themselves capable of long-term survival. In this study we investigate which types of genes are likely to generate functional and persistent duplicates. We demonstrate that genes that have generated duplicates in the C. elegans and S. cerevisiae genomes were 25%-50% more constrained prior to duplication than the genes that failed to leave duplicates. We further show that conserved genes have been consistently prolific in generating duplicates for hundreds of millions of years in these two species. These findings reveal one way in which gene duplication shapes the content of eukaryotic genomes. Our finding that the set of duplicate genes is biased has important implications for genome-scale studies.