With the aim of further exploiting the trade-off between formability and strength in Al alloys, this study addresses the influence of Cu in Al-Mg-Si alloys that achieve simultaneously high strength and high ductility via cluster hardening. The study carefully examines the mechanical properties and strain hardening behavior of various Mg/Si ratios with and without Cu and compares the effects of pre-aging and atypical long-term low-temperature aging treatments at 100°C to conventional heat treatments. Interestingly, in all cases adding Cu improved ductility. In the extremal case cluster hardening plus the addition of Cu quadruples elongation, while keeping yield strength similar to the classical T6 state. The results of the study are discussed with a focus on the dense distribution of clusters and partial hardening phases based on atom probe tomography data. Most importantly, the cluster-hardened alloys exhibit pronounced strain-hardening properties, which we evaluate using a Kocks-Mecking approach in combination with a microstructural analysis in the pre-aging and long-term aging condition. The key finding of the study involves the role of Cu in refining clusters/precipitates, where it causes a substantial increase in number density and volume fraction. This refinement, in combination with strain-induced clustering, contributes significantly to improving the alloys’ overall mechanical performance and underlines the central role of Cu in tailoring microstructural features, especially in alloys primarily strengthened by clusters.