A method is provided for planarizing a structure such as a shallow trench isolation region on a semiconductor substrate. A semiconductor substrate is provided having raised and lowered regions with substantially vertical and horizontal surfaces. The lowered regions may correspond to trench regions. The upper regions are covered by a masking layer of nitride having a predetermined thickness. Filler material such as non-conformal high density plasma oxide may be deposited over the horizontal surfaces to a thickness terminating within that of the thickness of the nitride layer. The raised regions of the filler material are then selectively removed in a single planarizing step without removing the filler material in the lowered regions using a fixed abrasive hard polishing pad, as opposed to an abrasive slurry.