  In this paper we show how the prediction of CMBR angular power spectra $C_l$
in non-Gaussian theories is affected by a cosmic covariance problem, that is
$(C_l,C_{l'})$ correlations impart features on any observed $C_l$ spectrum
which are absent from the average $C^l$ spectrum. Therefore the average
spectrum is rendered a bad observational prediction, and two new prediction
strategies, better adjusted to these theories, are proposed. In one we search
for hidden random indices conditional to which the theory is released from the
correlations. Contact with experiment can then be made in the form of the
conditional power spectra plus the random index distribution. In another
approach we apply to the problem a principal component analysis. We discuss the
effect of correlations on the predictivity of non-Gaussian theories. We finish
by showing how correlations may be crucial in delineating the borderline
between predictions made by non-Gaussian and Gaussian theories. In fact, in
some particular theories, correlations may act as powerful non-Gaussianity
indicators.
