Processes with significant transport delays in the input channel are commonly found in practice. The control of these processes is a challenging problem because of the difficulties in compensating the adverse effects induced by delayed control inputs. The aim of this paper is to show that high-order controllers can be required to obtain fast convergence rates in the face of significant transport delays. To this end, the control design is based on a sampled (discrete-time) version of the process dynamics where the sampling of the transport delay can be made in a straigthforward way. This model is then used to compute an output-feedback controller based on pole-placement polynomial methodologies. The resulting controller has the structure of a state-feedback controller equipped with integral action and a reduced-order observer to estimate unmeasured internal states. Numerical simulations are used to illustrate advantages and drawbacks of the use of high-order controllers to compensate transport delays.