When the amount of gravitational radiation is small, a binary system of two orbiting black holes evolves in a quasistationary manner. This system can be approximated by a linear combination of geometries each of which has standing waves at spatial infinity; however, the combination has purely outgoing radiation. A variational principle, for the geometries with standing waves, provides information about the binding energy, the stability of orbits, and the amplitude and frequency of gravitational radiation. For holes of equal mass starting at a large separation, approximately 3% of the initial mass is emitted as gravitational radiation before the evolution becomes so rapid that the quasistationary approximation fails.