A method for manufacturing parts is provided. The method includes cold rolling a substrate with work cylinders whose work surface has a roughness Ra2.5 of less than or equal to 3.6 μm, depositing the metal coating on at least one face of the annealed substrate by electrodeposition to form the metal sheet and deforming the cut metal sheet to form the parts. The outer surface of the metal coating has a waviness Wa0.8 of less than or equal to 0.5 μm after the deformation step. A part and vehicle are also provided.