A novel approach to control design for dead-time (DT) systems is proposed. The underlying idea is to treat the DT element not as a part of the generalized plant, but rather as a (causality) constraint imposed upon the controller (estimator). This enables one to use well-understood parametrizations of all delay-free controllers in the DT design. In particular, DT controllers can be extracted from such delay-free parametrizations. In this paper, the extraction procedures are developed in both H-2 and H-infinity settings. It is shown that the proposed approach yields simple solution procedures and new transparent and intuitively appealing structures for the resulting controllers and estimators.