Previous work has indicated that in calculating rates using activated-complex theory one should omit symmetry numbers from the rotational partition functions and multiply by a statistical factor; this factor is the number of equivalent forms of the activated complex that can arise from the reactants. This procedure can lead to error if the activated complex is chosen to have such a high degree of symmetry that it can form more than one form of the reactants or products. It is shown from a consideration of multi-dimensional potential-energy surfaces that a single activated complex cannot exist at the intersection of two valleys; three valleys, for example, will give rise to three separate activated states, each of which represents the lowest pass between a pair of valleys. The implications of this conclusion are considered with reference to several reactions, including that between hydrogen and iodine.