Glutarimide analogs, including thalidomide, redirect the E3 ubiquitin ligase CRL4CRBN to induce the ubiquitination and proteasomal degradation of specific zinc finger (ZF) proteins. While the core structural motif recognized by CRBN is characterized, it alone does not account for the full specificity of substrate recognition. To understand the impact of residues adjacent to the core motif, we constructed an extended ZF reporter library including all single ZFs and tandem ZF pairs in the human proteome totaling to 9,098 reporters from 1,655 ZF-containing proteins. We screened the activity of 29 glutarimide analogs against this ZF library leading to the identification and validation of compounds that collectively degrade 38 ZF reporters. High resolution cryo-electron microscopy and crystal structures of wild-type and mutant ZFs complexed with CRBN highlighted the significance of contacts outside the core ZF degron. We conducted systematic mutagenesis of both the ZFs and CRBN to investigate the role of individual amino acids and discovered that residues adjacent to the core ZF degron affect degradability, with single amino acid changes dictating drug specificity. Finally, we identified subtle chemical differences between glutarimide analogs that drastically broaden the target scope and redefine target selectivity. This study expands the scope of degradable ZF targets, including disease-driving transcription factors and provides a roadmap for the rational design of glutarimide analogs.