We consider a study of MZ and DZ twin pairs ascertained because one or both twins have a disease. Genotypes at a major locus are known and putative environmental risk factors have been measured for all individuals. The power of the study to estimate the effect on liability of the measured and residual genetic and environmental effects (Gm, Gr, Em, Er) and all two-way interactions between them (except Gr X Er) is estimated by simulation. If liabilities can be indexed on a continuous scale (eg, blood pressure as an index of liability to hypertension), then a study of 600 MZ and 600 DZ pairs would have sufficient power to detect quite subtle interaction effects, even if ascertainment is greatly biased toward MZ twins. If liabilities cannot be measured and only affection status is known, then the power of the study would be much lower, although not impracticably so. There appears to be no advantage in augmenting the twins with a sample of control individuals who have been drawn at random from the population regardless of disease status, at least for the case we have considered in which the disease threshold on the liability scale is assumed to be known without error. The argument is developed in terms of the utility of the design for research into breast cancer.