  Anisotropy data analysis leaves a significant degeneracy between primeval
spectral index (n_s) and cosmic opacity to CMB photons (\tau). Low--l
polarization measures, in principle, can remove it. We perform a likelihood
analysis to see how cosmic variance possibly affects such a problem. We find
that, for a sufficiently low noise level (\sigma_{pix}) and if \tau is not
negligibly low, the degeneracy is greatly reduced, while the residual impact of
cosmic variance on n_s and \tau determinations is under control. On the
contrary, if \sigma_{pix} is too high, cosmic variance effects appear to be
magnified. We apply general results to specific experiments and find that, if
favorable conditions occur, it is possible that a 2--\sigma detection of a
lower limit on \tau is provided by the SPOrt experiment. Furthermore, if the
PLANCK experiment will measure polarization with the expected precision, the
error on low--l harmonics is adequate to determine \tau, without significant
magnification of the cosmic variance. This however indicates that high
sensitivity might be more important than high resolution in \tau
determinations. We also outline that a determination of \tau is critical to
perform detailed analyses on the nature of dark energy and/or on the presence
of primeval gravitational waves.
