  We consider the evolution of supermassive black hole binaries at the center
of spherical, axisymmetric, and triaxial galaxies, using direct N-body
integrations as well as analytic estimates. We find that the rates of binary
hardening exhibit a significant N-dependence in all the models, at least for N
in the investigated range of 10^5<=N<=10^6. Binary hardening rates are also
substantially lower than would be expected if the binary loss cone remained
full, as it would be if the orbits supplying stars to the binary were being
efficiently replenished. The difference in binary hardening rates between the
spherical and nonspherical models is less than a factor of two even in the
simulations with the largest N. By studying the orbital populations of our
models, we conclude that the rate of supply of stars to the binary via draining
of centrophilic orbits is indeed expected to be much lower than the
full-loss-cone rate, consistent with our simulations. We argue that the
binary's evolution in the simulations is driven in roughly equal amounts by
collisional and collisionless effects, even at the highest N-values currently
accessible. While binary hardening rates would probably reach a limiting value
for large N, our results suggest that we cannot approach that rate with
currently available algorithms and computing hardware. The extrapolation of
results from N-body simulations to real galaxies is therefore not
straightforward, casting doubt on recent claims that triaxiality or axisymmetry
alone are capable of solving the final-parsec problem in gas-free galaxies.
