This paper analyses the relationship between the design and control of a heat-integrated distillation set-up consisting of a prefractionator and a side stream main column. The separation of a pentane-hexane-heptane mixture with moderate purity requirements is considered. Both forward and reverse heat-integration schemes are investigated. Different designs are possible, depending on the light/heavy split in the prefractionator and the heat-integration scheme. They are similar with respect to energy consumption, but very different with respect to dynamic behaviour. The differences are studied using frequency-dependent controllability analysis, as well as carrying out closed-loop simulation, in the presence of large feed composition disturbances. Thus, it is found that the forward heat-integration is much easier to control, using only temperature measurements. The low-cost design with a small prefractionator has the best closed-loop performance. The reverse heat-integration can be controlled only if a composition analyser of the side stream is available; a sharp light/heavy split in the prefractionator gives better disturbance rejection. The superior dynamic behaviour of the forward heat-integration scheme was confirmed by the study of a high purity separation of the benzene-toluene-xylene mixture.