  Viable modifications of gravity that may produce cosmic acceleration need to
be screened in high-density regions such as the Solar System, where general
relativity is well tested. Screening mechanisms also prevent strong anomalies
in the large-scale structure and limit the constraints that can be inferred on
these gravity models from cosmology. We find that by suppressing the
contribution of the screened high-density regions in the matter power spectrum,
allowing a greater contribution of unscreened low densities, modified gravity
models can be more readily discriminated from the concordance cosmology.
Moreover, by variation of density thresholds, degeneracies with other effects
may be dealt with more adequately. Specializing to chameleon gravity as a
worked example for screening in modified gravity, employing N-body simulations
of f(R) models and the halo model of chameleon theories, we demonstrate the
effectiveness of this method. We find that a percent-level measurement of the
clipped power at k < 0.3 h/Mpc can yield constraints on chameleon models that
are more stringent than what is inferred from Solar System tests or distance
indicators in unscreened dwarf galaxies. Finally, we verify that our method is
also applicable to the Vainshtein mechanism.
