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 \approx 0.72 + 0.32 ( s / m _ { H } ) , suggesting it is difficult ( though not excluded ) to end up with near maximally rotating holes from such scenarios .