A comparison of open-loop versus closed-loop identification when the identified model is used for control design, and when the true system belongs to the model class, is made. As a quality criterion of the model, the variance of the error between the output of the ideal closed loop system (with the ideal controller that would be designed if the true plant were known) and that of the model-based closed loop system (with the controller computed from the identified model) is chosen. It was shown that if the controller is a smooth function of the input-output dynamics and the disturbance spectrum, the best controller performance is achieved for the model obtained from closed-loop identification. Moreover, for minimum variance and model reference control design criteria it was established that the best controller for identification is the ideal controller. This ascertainment resulted in a suboptimal mixed open-loop/closed-loop identification scheme where the model is partly identified from closed-loop data, provided that the number of measurements is large enough.