Protein degradation by eukaryotic proteasomes is a multi-step process involving substrate recognition, ATP-dependent unfolding, translocation into the proteolytic core particle, and finally proteolysis. To date, most investigations of proteasome function have focused on the first and the last steps in this process. Here we examine the relationship between the stability of a folded protein domain and its degradation rate. Test proteins were targeted to the proteasome independently of ubiquitination by directly tethering them to the protease. Degradation kinetics were compared for test protein pairs whose stability was altered by either point mutation or ligand binding, but were otherwise identical. In both intact cells and in reactions using purified proteasomes and substrates, increased substrate stability led to an increase in substrate turnover time. The steady-state time for degradation ranged from ∼5 min (dihydrofolate reductase) to 40 min (I27 domain of titin). ATP turnover was 110/min./proteasome, and was not markedly changed by substrate. Proteasomes engage tightly folded substrates in multiple iterative rounds of ATP hydrolysis, a process that can be rate-limiting for degradation.