A process for manufacturing damascene wiring in integrated circuits is described. Trenches in the top most layer are first over-filled with a soft metal (such as copper) and then a relatively thin layer of a hard material such as tantalum, tantalum nitride, titanium, titanium nitride etc is deposited on the copper surface Under a first set of control conditions CMP is then applied for just long enough to selectively remove this hard material layer from peaks in the copper surface while leaving it intact in the valleys. The control conditions for CMP are then adjusted so that CMP can proceed with material at the peaks being removed at a significantly faster rate than in the valleys. Thus, when the point is reached that all copper outside the trenches has been removed, the trenches are found to be just filled with a flat layer that has no dishing.