A lower-bound renormalisation transformation of the type introduced by Kadanoff (see J. Statist. Phys., vol.14, p.171, 1976) is applied to the three-state Potts model. For both d=2 and d=3 the Kadanoff transformation predicts a continuous transition. Values for the critical exponents and the critical temperature are reported. The consistency of the d=2 results with series estimates gives the authors some confidence in the predictions for d=3.