A method of improving planarity of semiconductor wafer surfaces containing damascene and dual-damascene circuitry using chemical-mechanical polishing techniques. The method includes using a first polishing step to substantially remove excess surface metal up to a detected end point. After rinsing, a second step of chemical-mechanical polishing is applied, using a second slurry that has a higher selectivity for dielectric than metal, preferably from 1.8 to 4 or more times greater. The second step of polishing, in accordance with the invention, has been found to substantially eliminate dishing and improve planarity.