Abstract A weighted least-squares method for curve fitting multivariable, discrete-time transfer-function models from a known plant frequency response is presented. The algorithm supports the use of iterative, pre/post matrix-valued weighting functions, which commonly arise in control-relevant parameter estimation problems. A challenging case study involving an ill-conditioned , 40-tray high-purity binary distillation column model is presented. The closed-loop responses from the control-relevant model are superior to those obtained from unweighted multivariable estimation methods and one element-at-a-time estimation, in spite of the fact that these latter models display a closer ‘open-loop’ fit.