The variance is derived for narrow-band noise plus CW signal after detection and gating in time. The problem is solved for ideal and Gaussian filters with square-law and linear detection. The analysis is extended to a model filter in which the envelope of narrow-band noise plus signal is considered to be a function which is 1 constant for time intervals equal to the reciprocal of the noise bandwidth and 2 statistically independent in different intervals. Close agreement was obtained among all 3 filters. Graphs of the mean deviation divided by the mean power for noise alone are presented for the filters with square-law detection and predetection SNs of 0, 0.5, 1, and 2. A simplified model is considered in which the gate is assumed to start at a point of change in the model voltage. Tabulated values indicate that this model may be used for very large or very small gate widths, but that the discrepancy is large for gate widths of the order of the reciprocal of the noise bandwidth.