Using a phylogenetic model of evolution after genome duplication (i.e., polyploidy) and 12 yeast genomes with a shared genome duplication, I show that the loss of duplicate genes after that duplication occurred in three phases. First, losses that occurred immediately after the event were biased toward genes functioning in DNA repair and organellar functions. Then, the main group of duplicate losses appear to have been shaped by a requirement to maintain balance in protein levels: There is a strong statistical association between the number of protein interactions a gene's product is involved in and its propensity to have remained in duplicate. Moreover, when duplicated genes with interactions were lost, it was more common than expected for both members of an interaction pair to have been lost on the same branch of the phylogeny. Finally, in the third phase of the resolution process, overretention of duplicated enzymes carrying high flux and of duplicated genes involved in transcriptional regulation became dominant. I speculate that initial retention of such genes by a requirement to maintain gene dosage set the stage for the later functional changes that then maintained these duplicates for long periods.