Many reactions in enzymology are governed by the Michaelis–Menten equation. Characterising these reactions requires the estimation of the parameters KM and Vmax which determine the Michaelis–Menten equation and this is done by observing rates of reactions at a set of substrate concentrations. The choice of substrate concentrations is investigated by determining Bayesian D-optimal designs for a model in which residuals have a normal distribution with constant variance. Designs which focus on alternative quantities, such as KM or the ratio Vmax/KM are also considered. The effect on the optimal designs of alternative error distributions is also considered.