A controlled pressure regulation system generates the wafer-pressing pressures during a polishing operation. A wafer carrier head holds a wafer to be polished against a platen. A first and second pressure regulators respectively generate a first and second pressure onto the platen and the wafer carrier head to press the wafer to be polished. A first and second controllers are respectively connected to the first and second pressure regulators in control feedback loops to control the generation of the first and second pressures. The first and second pressures are controlled to obtain a desired difference of pressure between the first and second pressure.