Changes in gene expression play an important role in species' evolution. Earlier studies uncovered evidence that the effect of mutations on expression levels within the primate order is skewed, with many small downregulations balanced by fewer but larger upregulations. In addition, brain-expressed genes appeared to show an increased rate of evolution on the branch leading to human. However, the lack of a mathematical model adequately describing the evolution of gene expression precluded the rigorous establishment of these observations. Here, we develop mathematical tools that allow us to revisit these earlier observations in a model-testing and inference framework. We introduce a model for skewed gene-expression evolution within a phylogenetic tree and use a separate model to account for biological or experimental outliers. A Bayesian Markov chain Monte Carlo inference procedure allows us to infer the phylogeny and other evolutionary parameters, while quantifying the confidence in these inferences. Our results support previous observations; in particular, we find strong evidence for a sustained positive skew in the distribution of gene-expression changes in primate evolution. We propose a "corrective sweep" scenario to explain this phenomenon.