This contribution summarizes analytical properties of envelope modulation spectra of bandpass noise signals, which are relevant for the dependence of amplitude-modulation thresholds on modulation rate and noise carrier bandwidth. Lawson and Uhlenbeck [Threshold Signals (McGraw-Hill, New York)] showed in 1950 that the modulation spectrum, i.e., the power spectrum of the linear envelope of a bandpass noise, has an approximately triangular continuous spectrum besides the dc peak. For a constant overall level of a noise band, the total power of intrinsic noise fluctuations, i.e., the total area under the triangle, remains constant. The modulation spectrum, however, becomes broader with increasing noise bandwidth. For low modulation rates, this leads to a reduction in intrinsic modulation power. For higher modulation rates, the intrinsic modulation power increases. Simple analytical calculations are presented which compute the integrated modulation power of the noise within the transfer function of a hypothetical modulation filter. For a set of carrier bandwidths between 1 and 6000 Hz and for signal modulation of 5, 25, and 100 Hz the calculated values of overall modulation power are compared with experimentally obtained modulation detection thresholds, and with results from simulations of an auditory model.