The great majority of proteasome substrates are marked for degradation by the attachment of polyubiquitin chains. Ornithine decarboxylase is degraded by the proteasome in the absence of this modification. We previously showed that this mechanism of degradation was conserved in eukaryotic cells. Here we use a reporter destabilized by mouse ornithine decarboxylase to screen non-essential Saccharomyces cerevisiae deletion mutants. We identified novel mutants that affect both ubiquitin-dependent and -independent proteasome degradation pathways. YLR021W (IRC25/POC3) and YPL144W (POC4) encode interacting proteins that function in proteasome assembly, with putative homologues widespread among eukaryotes. Several additional mutants suffered from defects in proteasome-mediated proteolysis. These included mutants in the urmylation pathway of protein modification (but not the Urm1 modifier itself) and the Reg1 regulatory subunit of protein phosphatase 1. Finally, we noted increased rates of ornithine decarboxylase turnover in an rpn10Delta mutant in which the degradation of certain ubiquitinated substrates is impaired. Together, these results highlight the utility of a ubiquitin-independent degron in uncovering novel factors affecting general and substrate-specific proteasome function.