A mechanical polishing apparatus includes a polishing pad, at least one carrier head positioned over and off center relative to the polishing pad and configured for holding at least one substrate against the polishing pad within a first annular region of the polishing pad when the polishing pad is rotating. At least one conditioning head is positionable over and off center relative the polishing pad at a plurality of first positions and configured for applying a contacting surface of at least one conditioning pad against the polishing pad when the polishing pad is rotating, where the conditioning pad is applied to a second annular region of the polishing pad and moves between the plurality of first positions. In the apparatus, the diameter of the conditioning pad≦a difference between a radius of the polishing pad and a width of the first annular region.