This contribution investigates adaptive control of a First Order Plus Dead Time (FOPDT) system. An adaptive-control structure for dead-time compensation is justified by comparing it with a Smith predictor, and the justification for adaptation is explained with a simple example using arguments from Quantitative Feedback Theory. A novel identification algorithm is compared with two established ones by simulating them together with a FOPDT system in the considered adaptive-control structure. The simulations show that the modified scheme performs well compared to the established ones for the specific problem considered.