Internal model control (IMC) tuning rules have proven to yield acceptable performance and robustness properties when used in the control of typical processes (e.g., distillation columns, chemical reactors). In general, analytical IMC tuning rules are derived for proportional -integral (PI)/proportional-integral-derivative compensators by matching an approximate process model to a low-dimensional reference model. In the case of time-delay processes, an approximate model is obtained by taking a finite-dimensional approximation to the delay operator by means of Pade or Taylor expansions. For some typical cases arising commonly in process control, including first-order plus time-delay plants, this paper studies the optimality of PI-IMC tuning rules to match the prescribed closed-loop behavior (i.e., the reference model response). To this end, optimal PI settings are computed by means of numerical optimization based on random search algorithms. Small deviations of IMC tuning from optimality are found for moderate time delays. However, significant deviations are displayed for large time delays, which motivate the use of tuning techniques based on numerical optimization to refine IMC settings.