Proteins are targeted to the proteasome by the attachment of ubiquitin chains, which are markedly varied in structure. Three proteasome subunits-Rpn10, Rpn13, and Rpn1-can recognize ubiquitin chains. Here we report that proteins with single chains of K48-linked ubiquitin are targeted for degradation almost exclusively through binding to Rpn10. Rpn1 can act as a co-receptor with Rpn10 for K63 chains and for certain other chain types. Differences in targeting do not correlate with chain affinity to receptors. Surprisingly, in steady-state assays Rpn13 retarded degradation of various single-chain substrates. Substrates with multiple short ubiquitin chains can be presented for degradation by any of the known receptors, whereas those targeted to the proteasome through a ubiquitin-like domain are degraded most efficiently when bound by Rpn13 or Rpn1. Thus, the proteasome provides an unexpectedly versatile binding platform that can recognize substrates targeted for degradation by ubiquitin chains differing greatly in length and topology.