  Applying a transformation to a non-Gaussian field can enhance the information
content of the resulting power spectrum, by reducing the correlations between
Fourier modes. In the context of weak gravitational lensing, it has been shown
that this gain in information content is significantly compromised by the
presence of shape noise. We apply clipping to mock convergence fields, a
technique which is known to be robust in the presence of noise and has been
successfully applied to galaxy number density fields. When analysed in
isolation the resulting convergence power spectrum returns degraded constraints
on cosmological parameters. However substantial gains can be achieved by
performing a combined analysis of the power spectra derived from both the
original and transformed fields. Even in the presence of realistic levels of
shape noise, we demonstrate that this approach is capable of reducing the area
of likelihood contours within the $\Omega_m - \sigma_8$ plane by more than a
factor of three.
