Models for the interfrequency correlations among Fourier spectral ordinates and variances of these ordinates are presented. These covariances among Fourier spectral ordinates can be used to generate accelerograms within a stochastic simulation framework that offer improvements over traditional approaches that make use of deterministic Fourier amplitude spectra combined with a random phase spectrum. The article demonstrates that the accelerograms generated in this new way result in response spectral ordinates that have variances that are very consistent with those predicted by empirical ground‐motion models. In addition, the interperiod correlations among response spectral ordinates obtained from the simulated motions are also consistent with empirically derived response spectral correlations. The study partitions the variance among Fourier spectral ordinates into between‐event, between‐site and within‐event components, and interfrequency correlation models, and variance models are derived for each component. The between‐event correlations are found to exhibit a mild degree of magnitude dependence. An important feature of the new correlation and variance models is that they can be used to generate accelerograms that are broadly consistent with conditional response spectra. This new approach has significant implications for response‐history analyses within earthquake engineering that make use of conditional spectra as a target.