This work proposes a new and simple design for the filtered Smith predictor (FSP), which belongs to a class of dead-time compensators (DTCs) and allows the handling of stable, unstable, and integrative processes. For this purpose, first, to use lower-order controller and filters, it is shown that it is not necessary to use the integral action in the primary controller, which is used to tune the set-point response; then, the FSP filters are designed to obtain the desired disturbance rejection, robustness, and noise attenuation. Using this procedure, it is possible to obtain a better compromise between performance and complexity than other solutions in the literature. Two simulation case studies are used to compare the obtained solution with some recently published results. A practical experiment involving a neonatal intensive care unit is also presented to illustrate the usefulness of the proposed DTC.