The micromagnetic properties of a Ni film in a Cu/Ni crossed-wedge on Cu(0 0 1) are investigated by a combination of photoelectron emission microscopy and X-ray magnetic circular dichroism. Two spin-reorientation transitions (SRT) from in-plane to perpendicular to the film plane and back to in-plane were observed with increasing Ni thickness. Whereas no clear Cu thickness dependence of the former SRT has been observed, the latter strongly depends on Cu thickness, and is shifted to thinner Ni thicknesses by increasing Cu overlayer thickness. Furthermore, the size and the shape of the ferromagnetic domain structure in the perpendicular magnetization region also depend on Cu thickness. The average domain size decreases with increasing Ni thickness near the second SRT line. It is observed for the first time that these domain structure changes also depend on Cu overlayer thickness.