  Weak lensing is a potentially robust and model-independent cosmological
probe, but its accuracy is dependent on knowledge of the redshift distribution
of the source galaxies used. The most robust way to determine the redshift
distribution is via spectroscopy of a subsample of the source galaxies. We
forecast constraints from combining CMB anisotropies with cosmic shear using a
spectroscopically determined redshift distribution, varying the number of
spectra $N_{spec}$ obtained from 64 to $\infty$. The source redshift
distribution is expanded in a Fourier series, and the amplitudes of each mode
are considered as parameters to be constrained via both the spectroscopic and
weak lensing data. We assume independent source redshifts, and consider in what
circumstances this is a good approximation (the sources are clustered and for
narrow spectroscopic surveys with many objects this results in the redshifts
being correlated). It is found that for the surveys considered and for a prior
of 0.04 on the calibration parameters, the addition of redshift information
make significant improvements on the constraints on the cosmological
parameters; however, beyond $N_{spec}\sim$few$\times 10^3$ the addition of
further spectra will make only a very small improvement to the cosmological
parameters. We find that a better calibration makes large $N_{spec}$ more
useful. Using an eigenvector analysis, we find that the improvement continues
with even higher $N_{spec}$, but not in directions that dominate the
uncertainties on the standard cosmological parameters.
