The ubiquitin-dependent targeting of proteins to the proteasome is an essential mechanism for regulating eukaryotic protein stability. Here we define the minimal signal for the degradation of the S phase CDK inhibitor Sic1. Of 20 lysines scattered throughout Sic1, 6 N-terminal lysines serve as major ubiquitination sites. Sic1 lacking these lysines (K0N) is stable in vivo, but readdition of any one restores turnover. Nevertheless, ubiquitin chains attached at different N-terminal lysines specify degradation in vitro at markedly different rates. Moreover, although K0N can be ubiquitinated by SCF(Cdc4)/Cdc34 in vitro in the absence (but not in the presence) of S-CDK, it is degraded slowly. Our results reveal that a single multiubiquitin chain can sustain a physiological turnover rate, but that chain position plays an unexpectedly significant role in the rate of proteasomal proteolysis.