In the light of conflicting reports on the ability of copper(II) complexes of amyloid beta (Aβ) peptides to form ternary complexes with small molecules co-present in the biological milieu, we performed a study of coordination equilibria in the system containing Cu(II) ions, the Aβ1-16 peptide, glutamic acid and 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (2-[4-(2-hydroxyethyl)piperazin-1-yl]ethanesulfonic acid, HEPES) buffer. Using potentiometry, isothermal titration calorimetry (ITC), UV-visible spectroscopy and EPR, we concluded that glutamic acid was not able to form such a ternary complex, but can efficiently compete for the Cu(II) ion with the Aβ peptide at Glu concentrations relevant for the synaptic cleft. We also found that the literature constants for Cu(II) complexes with Glu were overestimated, but this effect was partially compensated by the formation of a ternary Cu(Glu)(HEPES) complex. Our results indicate that small molecules co-present with Cu(II) ions and Aβ peptides in the synaptic cleft are not very likely to enhance Cu(II)/Aβ interactions, but instead should be considered as a Cu(II) buffering system that may help prevent these interactions and participate in Cu(II) clearance from the synaptic cleft.