When planning a factorial experiment, it is often desirable (as pointed out by Yates (1937)) to include certain extra treatments falling outside the usual factorial scheme. I discuss here the exact analysis of an experiment of this type. Only standard principles of experimental analysis are involved, and the full exact analysis is not always required in practice, but the example may illustrate techniques that are useful in investigating more complicated designs that are sometimes encountered. I am grateful to the late Dr E. M. Crowther and Miss B. Benzian, of the Chemistry Department at Rothamsted, for discussion of the problem and for providing data for the illustrative example.