Next-generation T-cell therapies will likely continue to utilize T-cell receptors (TCRs) and chimeric antigen receptors (CARs) because each receptor type has advantages. TCRs often possess exceptional properties even when tested unmodified from patients' T cells. CARs are generally less sensitive, possibly because their ligand-binding domains are grafted from antibodies selected for binding affinity or avidity and not broadly optimized for a functional response. Because of the disconnect between binding and function among these receptor types, the ultimate potential of CARs optimized for sensitivity and selectivity is not clear. Here, we focus on a thoroughly studied immuno-oncology target, the HLA-A*02/HPV-E629-38 complex, and show that CARs can be optimized by a combination of high-throughput binding screens and low-throughput functional assays to have comparable activity to clinical TCRs in acute assays in vitro. These results provide a case study for the challenges and opportunities of optimizing high-performing CARs, especially in the context of targets utilized naturally by TCRs.