The interest for pure sulfide Cu(In,Ga)S2 chalcopyrite thin films is increasing again because their optical properties make them relevant candidates to be applied as top cell absorbers in tandem structures. Nonetheless, their use as so is still hindered by the level of single-junction cells performance achieved so far, which are far below those demonstrated by selenide absorbers. Amongst the reasons at the origin of the limited efficiency of Cu(In,Ga)S2-based solar devices, one can mention the poor tolerance of S-chalcopyrite to Cu deficiency. In fact, Cu-poor Cu(In,Ga)S2 films contain CuIn5S8 thiospinel secondary phase which is harmful for device performance. In the present work, we investigate Cu(In,Ga)S2 thin films grown by a modified three-stage process making use of graded indium and gallium fluxes during the first stage. The resulting absorbers are single phase and made of large grains extended throughout the entire film thickness. We propose that such a morphology is a proof of the recrystallization of the entire film during the synthesis. Devices prepared from those films and buffered with bath deposited CdS demonstrate outstanding efficiency of 16.0%. Replacing CdS by Zn(O,S) buffer layer leads to increased open circuit voltage and short circuit current; however, performance become limited by lowered fill factor.