We present a new approach to studying the evolution of massive black hole binaries in a stellar environment. By imposing conservation of total energy and angular momentum in scattering experiments, we find the dissipation forces that are exerted on the black holes by the stars, and thus obtain the decaying path of the binary from the classical dynamical friction regime down to subparsec scales. Our scheme lies between scattering experiments and N-body simulations. While still resolving collisions between stars and black holes, it is fast enough and allows us to use a large enough number of particles to reach a smooth and convergent result. We studied both an equal mass and a 10:1 mass ratio binaries under various initial conditions. We show that while an equal mass binary stalls at a nearly circular orbit, a runaway growth of eccentricity occurs in the unequal mass case. This effect reduces the time-scale for black hole coalescence through gravitational radiation to well below the Hubble time, even in spherical and gasless systems formed by dry mergers.