SCF ubiquitin ligases target phosphorylated substrates for ubiquitin-dependent proteolysis by means of adapter subunits called F-box proteins. The F-box protein Cdc4 captures phosphorylated forms of the cyclin-dependent kinase inhibitor Sic1 for ubiquitination in late G1 phase, an event necessary for the onset of DNA replication. The WD40 repeat domain of Cdc4 binds with high affinity to a consensus phosphopeptide motif (the Cdc4 phospho-degron, CPD), yet Sic1 itself has many sub-optimal CPD motifs that act in concert to mediate Cdc4 binding. The weak CPD sites in Sic1 establish a phosphorylation threshold that delays degradation in vivo, and thereby establishes a minimal G1 phase period needed to ensure proper DNA replication. Multisite phosphorylation may be a more general mechanism to set thresholds in regulated protein-protein interactions.