  Cosmological weak lensing gives rise to correlations in the ellipticities of
faint galaxies. This cosmic shear signal depends upon the matter power
spectrum, thus providing a means to constrain cosmological parameters. It has
recently been proposed that intrinsic alignments arising at the epoch of galaxy
formation can also contribute significantly to the observed correlations, the
amplitude increasing with decreasing survey depth. Here we consider the
two-point shear correlation function, and demonstrate that photometric redshift
information can be used to suppress the intrinsic signal; at the same time
Poisson noise is increased, due to a decrease in the effective number of galaxy
pairs. The choice to apply such a redshift-depending weighting will depend on
the characteristics of the survey in question. In surveys with a mean z of
about 1, although the lensing signal dominates, the measurement error bars may
soon become smaller than the intrinsic alignment signal; hence, in order not to
be dominated by systematics, redshift information in cosmic shear statistics
will become a necessity. We discuss various aspects of this.

Astrophysics