Techniques for polishing a wafer (10) include closed-loop control. The wafer can be held by a carrier head (100) having at least one chamber whose pressure is controlled to apply a downward force on the wafer. Thickness-related measurements of the wafer can be obtained during polishing and a thickness profile for the wafer is calculated based on the thickness-related measurements. The calculated thickness profile is compared to a target thickness profile. The pressure in at least one carrier head chamber is adjusted based on results of the comparison. The carrier head chamber pressures can be adjusted to control the amount of downward force applied to the wafer during polishing and/or to control the size of a loading area on the wafer against which the downward force is applied.