  The conformally flat families of initial data typically used in numerical
relativity to represent boosted black holes are not those of a boosted slice of
the Schwarzschild spacetime. If such data are used for each black hole in a
collision, the emitted radiation will be partially due to the ``relaxation'' of
the individual holes to ``boosted Schwarzschild'' form. We attempt to compute
this radiation by treating the geometry for a single boosted conformally flat
hole as a perturbation of a Schwarzschild black hole, which requires the use of
second order perturbation theory. In this we attempt to mimic a previous
calculation we did for the conformally flat initial data for spinning holes. We
find that the boosted black hole case presents additional subtleties, and
although one can evolve perturbatively and compute radiated energies, it is
much less clear than in the spinning case how useful for the study of
collisions are the radiation estimates for the ``spurious energy'' in each
hole. In addition to this we draw some lessons on which frame of reference
appears as more favorable for computing black hole collisions in the close
limit approximation.
