The tolerance of photovoltaic performances of Cu(In,Ga)Se2-based (CIGSe) solar cells prepared from 3-stage grown absorbers to cadmium sulfide (CdS) buffer layer thickness was investigated. We focus on the influence of the maximum Cu content y = [Cu]/([In]+[Ga]) reached during the co-evaporation process on this tolerance. By increasing the duration of the 2nd stage we varied ymax from 0.93±0.11 up to 1.06±0.12. Although final Cu content and CIGSe surface morphology seem to be similar for all absorbers, the photovoltaic performance of cells with higher maximum Cu content are better; moreover they tolerate much thinner CdS buffers (down to 10 nm-thick) without open circuit voltage or fill factor loss. Cells with lower ymax exhibit more erratic performance and J(V,T) measurements show a specific voltage distribution for thin CdS. From these results it appears possible to decrease the CdS buffer layer thickness if it is deposited on adapted absorbers.