Thalidomide analogues bind to cereblon (CRBN) and degrade specific C2H2 zing-finger (ZF)-containing proteins, highlighting a strategy to target this class of transcription factors. Sievers et al. screened the human C2H2 ZF proteome for degradation in the presence of thalidomide analogues and identified 11 ZF degrons. Structural analysis of these degrons followed by computational docking studies revealed that a large number of ZFs with diverse amino acid sequences are likely to bind to the drug–CRBN interface. Introducing specific chemical alterations into thalidomide analogues enabled selective degradation of distinct ZF targets.