A basic prediction of Green's [J. Acoust. Soc. Am. 32, 121--131 (1960)] classical energy-detection theory for Gaussian signals is a variance measure of stimulus fluctuation that decreases monotonically with the signal's duration-bandwidth product (TW). Experiments on intensity discrimination of narrow-band Gaussian noise provide the most direct support of this prediction for TW<~16, but indicate a need for another source of fluctuation for larger TW which could reflect internal noise [deBoer, J. Acoust. Soc. Am. 40, 552--560 (1966)]. An alternative solution is proposed based on detection of the largest waveform peak within the analysis window ((greater than or equal to)T). Investigation of this detector for narrow-band Gaussian noise shows that the variance (in dB) of the peak fluctuations is the sum of the variances of the classical energy fluctuation and of a waveform fluctuation due to random phases. For TW<20 the energy fluctuation dominates, while the waveform fluctuation dominates for larger TW. Predictions of the classical energy detection model with an internal noise of 1 dB are essentially indistinguishable from the peak detector model for intensity discrimination thresholds of narrow-band Gaussian noise; however, peak detection explains a wider range of experiments [Goldstein, J. Acoust. Soc. Am. 98, 2907(A) (1995)].