Cells must routinely recycle their proteins in order to maintain protein homeostasis and health. The bulk of protein turnover is facilitated by the proteasome and locally restricted within the center of the barrel-shaped 20S core. In order to be degraded, potential substrates must enter the core through an opening at the center of this complex. The pore is gated by N-terminal extensions that limit substrate entry and can be opened by native activators, which functionally regulate protein degradation. Gate-opening occurs through HbYX motifs at the extreme C-termini of proteasome activators. To date, characterization of the HbYX mechanism has been limited to protein-protein interactions of archaeal proteasome complexes. We have uncovered unexpected differences in the residue specificity of this motif for activating the human 20S proteasome. These sequence requirements are tuned by valency, which was generally corroborated by the C-termini of natural activators, providing insight into identifying new binding partners of the eukaryotic 20S proteasome. This work has established an alternative model to the HbYX mechanism for eukaryotic proteasome complexes. Finally, the Y motif offers an updated template for the design of pharmacological activators, critical protein-protein interface will deepen our understanding of proteasome biology and its implication in disease.