The quality of the data for system identification is of utmost of importance. Ideally, the output data should satisfy requirements regarding variance, and in the case of multiple-input multiple-output (MIMO) systems, correlation between the outputs. Usually, it is desired to achieve this by input perturbations with peak values as small as possible. A related measure is the crest factor, which is a measure of the (inverse) power of an input perturbation with given peak value. In this paper, the effect of minimizing the input peak and the crest factor, subject to desired output variances/covariances, is studied for various types of perturbation signals. The design procedure is completely data based; data are obtained by one or more preliminary experiments with the system to be identified. A model of an ill-conditioned distillation column is used for illustration.