The Hippo pathway controls cell homeostasis, and its deregulation can lead to human diseases. In this pathway, the YAP and TAZ transcriptional cofactors play a key role in stimulating gene transcription through their interaction with the TEAD transcriptional factors. Our study of YAP and TAZ peptides in biochemical and biophysical assays shows that both proteins have essentially the same affinity for TEAD. Molecular modeling and structural biology data suggest that they also bind to the same site on TEAD. However, this apparent similarity hides differences in the ways in which the two proteins interact with TEAD. The secondary structure elements of their TEAD binding site do not contribute equally to the overall affinity, and critical interactions with TEAD are made through different residues. This convergent optimization of the YAP/TAZ TEAD binding site suggests that the similarity in the affinities of binding of YAP to TEAD and of TAZ to TEAD is important for Hippo pathway functionality.