  We present a method for suppressing contributions from higher-order terms in
perturbation theory, greatly increasing the amount of information which may be
extracted from the matter power spectrum. In an evolved cosmological density
field the highest density regions are responsible for the bulk of the nonlinear
power. By suitably down-weighting these problematic regions we find that the
one- and two-loop terms are typically reduced in amplitude by ~70 per cent and
~95 per cent respectively, relative to the linear power spectrum. This greatly
facilitates modelling the shape of the galaxy power spectrum, potentially
increasing the number of useful Fourier modes by more than two orders of
magnitude. We provide a demonstration of how this technique allows the galaxy
bias and the amplitude of linear matter perturbations sigma_8 to be determined
from the power spectrum on conventionally nonlinear scales, 0.1<k<0.7 h/Mpc.
