The yeast protein Rad23 belongs to a diverse family of proteins that contain an amino-terminal ubiquitin-like (UBL) domain. This domain mediates the binding of Rad23 to proteasomes, which in turn promotes DNA repair and modulates protein degradation, possibly by delivering ubiquitinylated cargo to proteasomes. Here we show that Rad23 binds proteasomes by directly interacting with the base subcomplex of the regulatory particle of the proteasome. A component of the base, Rpn1, specifically recognizes the UBL domain of Rad23 through its leucine-rich-repeat-like (LRR-like) domain. A second UBL protein, Dsk2, competes with Rad23 for proteasome binding, which suggests that the LRR-like domain of Rpn1 may participate in the recognition of several ligands of the proteasome. We propose that the LRR domain of Rpn1 may be positioned in the base to allow the cargo proteins carried by Rad23 to be presented to the proteasomal ATPases for unfolding. We also report that, contrary to expectation, the base subunit Rpn10 does not mediate the binding of UBL proteins to the proteasome in yeast, although it can apparently contribute to the binding of ubiquitin chains by intact proteasomes.