All approaches to optimal experiment design for control have so far focused on deriving an input signal (or input signal spectrum) that minimizes some control-oriented measure of plant/model mismatch between the nominal closed loop system and the actual closed loop system, typically under a constraint on the total input power. In practical terms, this amounts to finding the (constrained) input signal that minimizes a measure of a control-oriented model uncertainty set. Here we address the experiment design problem from a "dual" point of view and in a closed-loop setting: given a maximum allowable control-oriented model uncertainty measure compatible with our robust control specifications, what is the cheapest identification experiment that will give us an uncertainty set that is within the required bounds? The identification cost can be measured by either the experiment time, the performance degradation due to the added excitation signal, or a combination of both. Our results are presented for the situation where the control objective is disturbance rejection only.