Recruitment of ubiquitinated proteins to the 26S proteasome lies at the heart of the ubiquitin-proteasome system (UPS). Genetic studies suggest a role for the multiubiquitin chain binding proteins (MCBPs) Rad23 and Rpn10 in recruitment, but biochemical studies implicate the Rpt5 ATPase. We addressed this issue by analyzing degradation of the ubiquitinated Cdk inhibitor Sic1 (UbSic1) in vitro. Mutant rpn10Delta and rad23Delta proteasomes failed to bind or degrade UbSic1. Although Rpn10 or Rad23 restored UbSic1 recruitment to either mutant, rescue of degradation by Rad23 uncovered a requirement for the VWA domain of Rpn10. In vivo analyses confirmed that Rad23 and the multiubiquitin binding domain of Rpn10 contribute to Sic1 degradation. Turnover studies of multiple UPS substrates uncovered an unexpected degree of specificity in their requirements for MCBPs. We propose that recruitment of substrates to the proteasome by MCBPs provides an additional layer of substrate selectivity in the UPS.