Upon binding to thalidomide and other immunomodulatory drugs, the E3 ligase substrate receptor cereblon (CRBN) promotes proteosomal destruction by engaging the DDB1-CUL4A-Roc1-RBX1 E3 ubiquitin ligase in human cells but not in mouse cells, suggesting that sequence variations in CRBN may cause its inactivation. Therapeutically, CRBN engagers have the potential for broad applications in cancer and immune therapy by specifically reducing protein expression through targeted ubiquitin-mediated degradation. To examine the effects of defined sequence changes on CRBN's activity, we performed a comprehensive study using complementary theoretical, biophysical, and biological assays aimed at understanding CRBN's nonprimate sequence variations. With a series of recombinant thalidomide-binding domain (TBD) proteins, we show that CRBN sequence variants retain their drug-binding properties to both classical immunomodulatory drugs and dBET1, a chemical compound and targeting ligand designed to degrade bromodomain-containing 4 (BRD4) via a CRBN-dependent mechanism. We further show that dBET1 stimulates CRBN's E3 ubiquitin-conjugating function and degrades BRD4 in both mouse and human cells. This insight paves the way for studies of CRBN-dependent proteasome-targeting molecules in nonprimate models and provides a new understanding of CRBN's substrate-recruiting function.