Summary: In linear models the breakdown point of an estimator depends strongly on the underlying design. This holds in particular for high breakdown point estimators as the least median of squares estimators or least trimmed squares estimators. It could be shown that the breakdown point is maximized if the number of regressors which lie in a subspace is minimized. This means in particular that the number of repetitions of experimental conditions should be minimized. Usually this leads to designs which are very different from the classically optimal designs. But in some situations breakdown point maximizing designs can be found which are also optimal in the classical sense. In this paper two examples are given where breakdown point maximizing designs are also classically optimal.