  Recently, it has been shown that cross-correlating CMB lensing and 3D cosmic
shear allows to considerably tighten cosmological parameter constraints. We
investigate whether similar improvement can be achieved in a conventional
tomographic setup. We present Fisher parameter forecasts for a Euclid-like
galaxy survey in combination with different ongoing and forthcoming CMB
experiments. In contrast to a fully three-dimensional analysis we find only
marginal improvement. Assuming Planck-like CMB data we show that including the
full covariance of the combined CMB and cosmic shear data improves the dark
energy figure of merit by only three per cent. The marginalized error on the
sum of neutrino masses is reduced at the same level. For a next generation CMB
satellite mission such as Prism the predicted improvement of the dark energy
figure of merit amounts to approximately 25 per cent. Furthermore, we show that
the small improvement is contrasted by an increased bias in the dark energy
parameters when the intrinsic alignment of galaxies is not correctly accounted
for in the full covariance matrix.
