A lapping control system for a row of thin film magnetic transducers formed on a substrate. Each of the rows comprises a plurality of thin film magnetic transducers and at least two test structures. Each test structure has at least two elements which comprises some combination of switch elements or test thin film magnetic transducers. As the row of transducers is lapped, each time one of the switch elements is opened, the saturation current (ISAT) of one or more of the thin film magnetic transducers is measured and recorded so that a correlation between ISAT and throat height of the transducers is established during lapping. This correlation is used to establish the point at which lapping should be terminated.