The proteasome controls the turnover of many cellular proteins. Two structural features are typically required for proteins to be degraded: covalently attached ubiquitin polypeptides that allow binding to the proteasome and an unstructured region in the targeted protein that initiates proteolysis. Here, we have tested the degradation of model proteins to further explore how the proteasome selects its substrates. Using purified yeast proteasome and mammalian proteasome in cell lysate, we have demonstrated that the two structural features can act in trans when separated onto different proteins in a multisubunit complex. In such complexes, the location of the unstructured initiation site and its chemical properties determine which subunit is degraded. Thus, our findings reveal the molecular basis of subunit specificity in the degradation of protein complexes. In addition, our data provide a plausible explanation for how adaptor proteins can bind to otherwise stable proteins and target them for degradation.