  We consider corrections to the underlying cosmology due to secondary
contributions from weak gravitational lensing, the integrated Sachs-Wolfe
effect, and the Sunyaev-Zel'dovich effect contained in the trispectrum. We
incorporate these additional contributions to the covariance of a binned
angular power spectrum of temperature anisotropies in the analysis of current
and prospective data sets. Although recent experiments such as ACBAR and CBI
are not particularly sensitive to these additional non-Gaussian effects, the
interpretation of Planck and CMBPol anisotropy spectra will require an
accounting of non-Gaussian covariance leading to a degradation in cosmological
parameter estimates by up to 20% and 30%, respectively.
