  We compute the gravitational radiation generated in the evolution of a family
of close binary black hole configurations, using a combination of numerical and
perturbative approximation methods. We evolve the binaries with spins, $s$,
aligned or counter-aligned with the orbital angular momentum from near the
innermost stable circular orbit (ISCO) down to the final single rotating black
hole. For the moderately spinning holes studied here the remnant Kerr black
hole formed at the end of an inspiral process have a rotation parameter
$a/M\approx0.72+0.32(s/m_H)$, suggesting it is difficult (though not excluded)
to end up with near maximally rotating holes from such scenarios.
