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Experiments having two treatment factors and one blocking factor are considered in which a particular combination of treatment factor levels must be excluded. The motivation for the work is a medical trial of two drugs in which a double placebo cannot be administered on ethical grounds. The contrasts of interest compare the effects of having both treatment factors at non–zero labelled levels with the effects of having only one treatment factor at a non–zero labeled level. A lower bound is derived on the average variance of the contrast estimators n x m experiments. For n×2 experiments a balance property is defined which is possessed by many efficient designs. Designs having the property are characterized through the structure of the intra–block information matrix. Efficient reinforced group divisible designs are constructed and assessed against the lower bound.<\div>

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