An efficient yet simple automatic tuning algorithm is developed for dead-time compensators (DTC) common to industrial process controllers. The auto-tuner is capable of setting eight tuning parameters : two for the primary controller, three for the process model and another three for an additional modification aimed at improving the disturbance rejection properties. The process model used in the algorithm is a first order + dead time which captures the essential dynamics of the majority of loops in the chemical and process industries. The methodology and methods used, however, can be readily extended to higher order and more complicated models. The auto-tuner utilizes two points on the process Nyquist curve acquired through automatically generated controlled limit cycles in closed loop fashion. Least squares is then used to estimate the process model. It is shown that an appropriate selection of the two points as well as the weighting matrix in the least squares leads to a robust estimation. A simple rule based on robustness considerations is employed by the auto-tuner for tuning the primary controller. The complete auto-tuners fit easily into existing micro-processor-based industrial controllers. Simulations demonstrate the effectiveness and robustness of the auto-tuner as well as the improved performance gained by the automatically-tuned DTC for high-order processes and even for dead-time free processes though it contains a simple model.