  Quantum field theories at finite matter densities generically possess a
partition function that is exponentially suppressed with the volume compared to
that of the phase quenched analogue. The smallness arises from an almost
uniform distribution for the phase of the fermion determinant. Large
cancellations upon integration is the origin of a poor signal to noise ratio.
We study three alternatives for this integration: the Gaussian approximation,
the "telegraphic" approximation, and a novel expansion in terms of
theory-dependent moments and universal coefficients. We have tested the methods
for QCD at finite densities of heavy quarks. We find that for two of the
approximations the results are extremely close - if not identical - to the full
answer in the strong sign problem regime.
