  For two-black-hole time-symmetric initial data we consider the Corvino
construction of gluing an exact Schwarzschild end. We propose to do this by
using Brill waves. We address the question of whether this method can be used
to reduce the overall energy, which seems to relate to the question of whether
it can reduce the amount of `spurious' gravitational radiation. We find a
positive answer at first order in the inverse gluing radius.
