In this paper, the performance deterioration of optimal regulators caused by the introduction of deterministic state-estimators such as Kalman estimators and Luenberger observers is investigated. It is shown that, in the case of Kalman estimators, the performance deterioration cannot be made arbitrarily small unless the optimal control law can be implemented by direct output feedback. In the case of Luenberger observers with minimum order, a necessary and sufficient condition for the performance deterioration to be made arbitrarily small is derived.