In model predictive control one often needs a finite impulse response (FIR) or step response model of the process. Several algorithms have been proposed for the direct identification of these nonparsimonious models (least-squares and biased algorithms such as regularized least squares and partial least squares). These algorithms are compared from several points of view : the closeness of the fit to the true model, the level of robust stability provided by the identified model, and the actual control performance obtained using the identified models. Although there are conveniences in directly identifying such nonparsimonious models (i.e., they can fit any complex dynamic system; there is no need for model structure selection), there are many disadvantages. In comparison with identifying parsimonious transfer function models by prediction error methods and then obtaining the impulse response from them, even the best direct FIR identification methods will generally provide much worse results or require much more data to achieve comparable results. Although many of these points are appreciated in a general way by the control community, this paper tries to quantify them on a reasonable basis.