I here estimate the energy cost of changes in gene expression for several thousand genes in the yeast Saccharomyces cerevisiae. A doubling of gene expression, as it occurs in a gene duplication event, is significantly selected against for all genes for which expression data is available. It carries a median selective disadvantage of s > 10(-5), several times greater than the selection coefficient s = 1.47 x 10(-7) below which genetic drift dominates a mutant's fate. When considered separately, increases in messenger RNA expression or protein expression by more than a factor 2 also have significant energy costs for most genes. This means that the evolution of transcription and translation rates is not an evolutionarily neutral process. They are under active selection opposing them. My estimates are based on genome-scale information of gene expression in the yeast S. cerevisiae as well as information on the energy cost of biosynthesizing amino acids and nucleotides.