The invention relates to improvements in the polishing of a layer of germanium by a method which includes a first step of chemical-mechanical polishing of the surface of the germanium layer that is carried out with a first polishing solution having an acidic pH. The first polishing step is then followed by a second step of chemical-mechanical polishing of the surface of the germanium layer carried out with a second polishing solution having an alkaline pH. The polished heteroepitaxial germanium layer has a surface microroughness of less than 0.1 nm RMS and a surface macroroughness corresponding to a surface haze level of less than 0.5 ppm.