Abstract: A CMP polishing head having multiple concentric pressure zones for selectively increasing polishing pressure against selected regions of a semiconductor wafer in order to compensate for variations in polishing rates on the wafer surface otherwise caused by ridges or other non-uniformities in the wafer surface. The polishing head of the present invention comprises multiple, concentric, inflatable pressure rings each of which may be selectively inflated to increase the polishing pressure against a concentric ridge or material elevation on the corresponding concentric region of the wafer surface and increase the polishing rate of the concentric ridge or elevation between the rotating polishing head and a stationary polishing pad. A channel selector may be included in the polishing head for selectively aligning an air/pressure vacuum source with a selected one of multiple pressure tubes that connect to the respective pressure rings.