An apparatus and method of lapping of rows of magnetic recording heads uses multiple fluid-filled ports with variable pressure against a flexible adhesive tape to secure to and support the row. The tape provides the necessary tangential restraining force to drag the workpiece along a lapping plate. The multiple ports beneath the tape provide the necessary normal force to press the workpiece against the lapping plate to allow lapping to occur. The amount of material removal from the row is varied by adjusting the pressure in the ports such that higher pressure is applied to those heads with higher stripe height, and lower pressure is applied to recording heads with lower stripe height. To set or adjust the port. pressures, measurements of the read sensor resistance are taken to calculate the stripe height. The stripe height is roughly proportional to the reciprocal of resistance.