The catalytic redox activity of Cu(II) bound to the amino-terminal copper and nickel (ATCUN) binding motif (Xxx-Zzz-His, XZH) is stimulating the development of catalytic metallodrugs based on reactive oxygen species (ROS)-mediated biomolecule oxidation. However, low Cu(I) availability resulting from the strong Cu(II) binding affinity of the ATCUN motif is regarded as a limitation to efficient ROS generation. To address this, we replaced the imidazole moiety (pKa 7.0) of Gly-Gly-His-NH2 (GGHa, a canonical ATCUN peptide) with thiazole (pKa 2.7) and oxazole (pKa 0.8), yielding GGThia and GGOxa, respectively. A newly synthesized amino acid, Fmoc-3-(4-oxazolyl)-l-alanine, served as a histidine surrogate featuring an azole ring with the lowest pKa among known analogues. Despite similar square-planar Cu(II)-N4 geometries being observed for the three Cu(II)-ATCUN complexes by electron paramagnetic resonance spectroscopy and X-ray crystallography, the azole modification enabled the Cu(II)-ATCUN complexes to exhibit significant rate enhancement for ROS-mediated DNA cleavage. Further analyses based on Cu(I)/Cu(II) binding affinities, electrochemical measurements, density functional theory calculations, and X-ray absorption spectroscopy indicated that the azole modification enhanced the accessibility of the Cu(I) oxidation state during ROS generation. Our oxazole/thiazole-containing ATCUN motifs provide a new design strategy for peptide ligands with modulated N donor ability, with potential applications in the development of ROS-mediated metallodrugs.