  The Bowen-York initial value data typically used in numerical relativity to
represent spinning black hole are not those of a constant-time slice of the
Kerr spacetime. If Bowen-York initial 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 Kerr form. We compute this radiation by treating the
geometry for a single hole as a perturbation of a Schwarzschild black hole, and
by using second order perturbation theory. We discuss the extent to which
Bowen-York data can be expected accurately to represent Kerr holes.
