Whole-genome duplications (WGDs) have contributed to gene-repertoire enrichment in many eukaryotic lineages. However, most duplicated genes are eventually lost and it is still unclear why some duplicated genes are evolutionary successful whereas others quickly turn to pseudogenes. Here, we show that dosage constraints are major factors opposing post-WGD gene loss in several Paramecium species that share a common ancestral WGD. We propose a model where a majority of WGD-derived duplicates preserve their ancestral function and are retained to produce enough of the proteins performing this same ancestral function. Under this model, the expression level of individual duplicated genes can evolve neutrally as long as they maintain a roughly constant summed expression, and this allows random genetic drift toward uneven contributions of the two copies to total expression. Our analysis suggests that once a high level of imbalance is reached, which can require substantial lengths of time, the copy with the lowest expression level contributes a small enough fraction of the total expression that selection no longer opposes its loss. Extension of our analysis to yeast species sharing a common ancestral WGD yields similar results, suggesting that duplicated-gene retention for dosage constraints followed by divergence in expression level and eventual deterministic gene loss might be a universal feature of post-WGD evolution.