The progressive, neurodegenerative Alzheimer’s disease (AD) is the most widespread dementia. Due to the ageing of the population and the current lack of molecules able to prevent or stop the disease, AD will be even more impactful for society in the future. AD is a multifactorial disease, and, among other factors, metal ions have been regarded as potential therapeutic targets. This is the case for the redox-competent Cu ions involved in the production of reactive oxygen species (ROS) when bound to the Alzheimer-related Aβ peptide, a process that contributes to the overall oxidative stress and inflammation observed in AD. Here, we made use of peptide ligands to stop the Cu(Aβ)-induced ROS production and we showed why the AHH sequence is fully appropriate, while the two parents, AH and AAH, are not. The AHH peptide keeps its beneficial ability against Cu(Aβ)-induced ROS, even in the presence of ZnII-competing ions and other biologically relevant ions. The detailed kinetic mechanism by which AHH could exert its action against Cu(Aβ)-induced ROS is also proposed.