This paper is intended to answer the question: "When can a simple dead-time compensator be expected to perform better than a PID?". The performance criterion used is the integrated absolute error (IAE). It is compared for PI and PID controllers and a simple dead-time compensator (DTC) when a step load disturbance is applied at the plant input. Both stable and integrating processes are considered. For a fair comparison the controllers should provide equal robustness in some sense. Here, as a measure of robustness, the H-infinity norm of the sum of the absolute values of the sensitivity function and the complementary sensitivity function is used. Performance of the DTC's is given also as a function of dead-time margin (D-M).