In this contribution, the variance properties of a two-step ARX estimation scheme are discussed. An expression for the covariance of the final low-order model is calculated and it is shown how this covariance can be minimised (at least for high-model orders). The implication of the results is that identification of the dynamics of a system can very easily be performed with standard linear least squares (two times), even if the measurement noise is heavily colored. A numerical example is included, where this two-step method gives a variance which is close (but not equal) to the Cramèr-Rao lower bound. Moreover, the point estimate of the covariance is close to the one obtained through Monte Carlo simulations.