This paper deals with the problem of reducing the complexity of linear, time-invariant and dynamic systems which are described by input-output data corrupted by noise. The goal of the modelling procedure is to choose a model of low order such that the ‘ worst-case ’ error with respect to the unknown system is minimized when the input runs over a given set. An algorithm is given for the computation of the optimal model and of the error bounds according to the disturbance characteristics.