in [1] f. sterreicher described a method to construct a least favourable pair of distributions for testing problems where one hypothesis is simple and the other composite of the contamination neighbourhood type. applying this construction two times successively sterreicher, obtains a least favourable pair of distributions also for the case, where both hypotheses are composite of the contamination neighbourhood type. this method of construction, though working in principle, is rather unwieldy in practical applications.

In this present paper the method of construction is modified so as to give a least favourable pair for the composite-composite problem in one single step of construction. Especially for the construction of robust test in practical applications this method is shown to by very simple.