Targeted protein degradation is a promising therapeutic strategy, spearheaded by the anti-myeloma drugs lenalidomide and pomalidomide. These drugs stabilize very efficiently the complex between the E3 ligase Cereblon (CRBN) and several non-native client proteins (neo-substrates), including the transcription factors Ikaros and Aiolos and the enzyme Caseine Kinase 1α (CK1α,), resulting in their degradation. Although the structures for these complexes have been determined, there are no evident interactions that can account for the high efficiency of formation of the ternary complex. We show that lenalidomide's stabilization of the CRBN-CK1α complex is largely due to hydrophobic shielding of intermolecular hydrogen bonds. We also find a quantitative relationship between hydrogen bond robustness and binding affinities of the ternary complexes. These results pave the way to further understand cooperativity effects in drug-induced protein-protein complexes and could help in the design of improved molecular glues and more efficient protein degraders.