Innermost stable circular orbit of binary black holes

We introduce a new method to construct solutions to the constraint equations of general relativity describing binary black holes in quasicircular orbit. Black hole pairs with arbitrary momenta can be constructed with a simple method recently suggested by Brandt and Br\"ugmann, and quasicircular orbits can then be found by locating a minimum in the binding energy along sequences of constant horizon area. This approach produces binary black holes in a ``three-sheeted'' manifold structure, as opposed to the ``two-sheeted'' structure in the conformal-imaging approach adopted earlier by Cook. We focus on locating the innermost stable circular orbit and compare with earlier calculations. Our results confirm those of Cook and imply that the underlying manifold structure has a very small effect on the location of the innermost stable circular orbit.