Toy power spectra drawn from a Gaussian distribution with mean given by a ΛCDM power spectrum and a covariance given by the band-averaged C_ℓ covariance matrix, (top), and the corresponding differences with respect to the input ΛCDM model. Note the apparent presence of “coherent oscillatory features” in the difference spectra. These are fully described by the power spectrum covariance matrix. To assess the statistical significance of apparently “unexpected features” in the power spectrum, it is critical to include all sources of correlations among different C_ℓ’s.