The minimum measurement time needed to obtain a given variance in the mean power measurement is determined for feedback-controlled electrical substitution radiometers by combining previous results for response time and noise power gain with the variance in the mean of a sequence of N partially correlated observations. For large N and high sampling frequencies it is asymptotic to Lambda/2 in units of the detector time constant, where Lambda is the ratio of the square of the detector noise equivalent power to the desired variance in the mean power measurement. For a second-order system the optimum measurement time for repeated observations is typically 1.4-1.7 times smaller than that for a single observation.