Inhibiting protein function selectively is a major goal of modern drug discovery. Here, we report a previously understudied benefit of small molecule proteolysis-targeting chimeras (PROTACs) that recruit E3 ubiquitin ligases to target proteins for their ubiquitination and subsequent proteasome-mediated degradation. Using promiscuous CRBN- and VHL-recruiting PROTACs that bind >50 kinases, we show that only a subset of bound targets is degraded. The basis of this selectivity relies on protein-protein interactions between the E3 ubiquitin ligase and the target protein, as illustrated by engaged proteins that are not degraded as a result of unstable ternary complexes with PROTAC-recruited E3 ligases. In contrast, weak PROTAC:target protein affinity can be stabilized by high-affinity target:PROTAC:ligase trimer interactions, leading to efficient degradation. This study highlights design guidelines for generating potent PROTACs as well as possibilities for degrading undruggable proteins immune to traditional small-molecule inhibitors.