A fundamental question in feedback control is: How does the feedback affect the sensitivity of the system’s motion to small variations of the system’s parameters? This question is investigated for a sufficiently smooth Bolza optimization problem. A necessary and sufficient condition is derived for closed loop sensitivity reduction according to an inequality involving a particular integral-square sensitivity measure that is closely related to Bode’s classical sensitivity function. This condition, under a mild assumption, holds for problems that are separable in the state and control variables: The results are specialized for linear problems.