  Black hole binaries on non-eccentric orbits form an important subclass of
gravitational wave sources, but it is a non-trivial issue to construct
numerical initial data with minimal initial eccentricity for numerical
simulations. We compute post-Newtonian orbital parameters for quasi-spherical
orbits using the method of Buonanno, Chen and Damour (2006) and examine the
resulting eccentricity in numerical simulations. Four different methods are
studied resulting from the choice of Taylor-expanded or effective-one-body
Hamiltonians, and from two choices for the energy flux. The eccentricity
increases for unequal masses and for spinning black holes, but remains smaller
than that obtained from previous post-Newtonian approaches. The
effective-one-body Hamiltonian offers advantages for decreasing initial
separation as expected, but in the context of this study also performs
significantly better than the Taylor-expanded Hamiltonian for binaries with
spin.
