Cell cycle progression depends on precise elimination of cyclins and cyclin-dependent kinase (CDK) inhibitors by the ubiquitin system. Elimination of the CDK inhibitor Sic1 by the SCFCdc4 ubiquitin ligase at the onset of S phase requires phosphorylation of Sic1 on at least six of its nine Cdc4-phosphodegron (CPD) sites. A 2.7 A X-ray crystal structure of a Skp1-Cdc4 complex bound to a high-affinity CPD phosphopeptide from human cyclin E reveals a core CPD motif, Leu-Leu-pThr-Pro, bound to an eight-bladed WD40 propeller domain in Cdc4. The low affinity of each CPD motif in Sic1 reflects structural discordance with one or more elements of the Cdc4 binding site. Reengineering of Cdc4 to reduce selection against Sic1 sequences allows ubiquitination of lower phosphorylated forms of Sic1. These features account for the observed phosphorylation threshold in Sic1 recognition and suggest an equilibrium binding mode between a single receptor site in Cdc4 and multiple low-affinity CPD sites in Sic1.