Peptide-based compounds including heteroatom-containing, three-membered rings efficiently and selectively inhibit specific activities of N-terminal nucleophile (Ntn) hydrolases. The activities of those Ntn having multiple activities can be differentially inhibited by the compounds described. For example, the chymotrypsin-like and PGPH activities of the 20S proteasome can be selectively inhibited with the inventive compounds. The peptide-based compounds include at least three peptide units, an epoxide or aziridine, and functionalization at the N-terminus, such as a detectable label. Along with therapeutic utilities, these peptide based compounds can be used in assays useful for screening, monitoring, diagnostic and/or dosing purposes.