  We consider the initial data problem for several black holes in vacuum with
arbitrary momenta and spins on a three space with punctures. We compactify the
internal asymptotically flat regions to obtain a computational domain without
inner boundaries. When treated numerically, this leads to a significant
simplification over the conventional approach which is based on throats and
isometry conditions. In this new setting it is possible to obtain existence and
uniqueness of solutions to the Hamiltonian constraint.
