  We present a simple method for \emph{a posteriori} removal of a significant
fraction of the density-fitting error from the calculated total coupled-cluster
energies. The method treats the difference between the exact and density-fitted
integrals as a perturbation, and simplified response-like equations allow to
calculate improved amplitudes and the corresponding energy correction. The
proposed method is tested at the coupled-cluster singles and doubles level of
theory for a diverse set of moderately-sized molecules. On average, error
reductions by a factor of approximately ten and twenty are observed in
double-zeta and triple-zeta basis sets, respectively. Similar reductions are
observed in calculations of interaction energies of several model complexes.
The computational cost of the procedure is small in comparison with the
preceding coupled-cluster iterations. The applicability of the method is not
limited to the density-fitting approximation; in principle, it can be used in
conjunction with an arbitrary decomposition scheme of the electron repulsion
integrals.
