During planarization of wafers, the thickness of a layer of a wafer is measured at a number of locations, after the wafer has been planarized by chemical mechanical polishing. The thickness measurements are used to automatically determine, from a center to edge profile model to which the measurements are fit, a parameter that controls chemical mechanical polishing, called “backside pressure.” Backside pressure is determined in some embodiments by a logic test based on the center-to-edge profile model, coefficient of determination R-square of the model, and current value of backside pressure. Note that a “backside pressure” set point is adjusted only if the fit of the measurements to the model is good, e.g. as indicated by R-square being greater than a predetermined limit. Next, the backside pressure that has been determined from the model is used in planarizing a subsequent wafer.