  Context. Weak gravitational lensing is a powerful probe of large-scale
structure and cosmology. Most commonly, second-order correlations of observed
galaxy ellipticities are expressed as a projection of the matter power
spectrum, corresponding to the lowest-order approximation between the projected
and 3d power spectrum.
  Aims. The dominant lensing-only contribution beyond the zero-order
approximation is the reduced shear, which takes into account not only
lensing-induced distortions but also isotropic magnification of galaxy images.
This involves an integral over the matter bispectrum. We provide a fast and
general way to calculate this correction term.
  Methods. Using a model for the matter bispectrum, we fit elementary functions
to the reduced-shear contribution and its derivatives with respect to
cosmological parameters. The dependence on cosmology is encompassed in a
Taylor-expansion around a fiducial model.
  Results. Within a region in parameter space comprising the WMAP7 68% error
ellipsoid, the total reduced-shear power spectrum (shear plus fitted
reduced-shear correction) is accurate to 1% (2%) for l<10^4 (l<2x10^5). This
corresponds to a factor of four reduction of the bias compared to the case
where no correction is used. This precision is necessary to match the accuracy
of current non-linear power spectrum predictions from numerical simulations.
