The proteasome controls the concentrations of most proteins in eukaryotic cells. It recognizes its protein substrates through ubiquitin tags and initiates degradation at disordered regions within the substrate. Here we show that the proteasome has pronounced preferences for the amino acid sequence of the regions at which it initiates degradation. Specifically, proteins in which the initiation regions have biased amino acid compositions show longer half-lives in yeast than proteins with unbiased sequences in the regions. The relationship is also observed on a genomic scale in mouse cells. These preferences affect the degradation rates of proteins in vitro, can explain the unexpected stability of natural proteins in yeast and may affect the accumulation of toxic proteins in disease. We propose that the proteasome's sequence preferences provide a second component to the degradation code and may fine-tune protein half-life in cells.