PA28 (also named REG or 11S) is a ring-shaped (180-kDa) interferon-gamma-induced complex that associates with the 20S proteasome and dramatically stimulates the breakdown of short peptides. Immunoprecipitation studies indicate that in vivo PA28 also exists in larger complexes that also contain the 19S particle, which is required for the ATP-ubiquitin-dependent degradation of proteins. However, because of its lability (e.g., it does not withstand exposure to high ionic strength buffers), this larger complex cannot be purified by standard biochemical protocols. Therefore, we developed a method to reconstitute in vitro such hybrid proteasomes (i.e., PA28-20S-19S) from highly purified components. This chapter describes conditions that allow the association of PA28 with "singly capped" 26S (i.e., 19S-20S) particles. In addition assays are described to measure absolute rates of degradation of several nonubiquitinated proteins by 26S and 20S proteasomes and methods to analyze the pattern and size distribution of peptides generated during the degradation of these proteins.