  We study the long-term evolution of massive black hole binaries (MBHBs) at
the centers of galaxies using detailed scattering experiments to solve the full
three-body problem. Ambient stars drawn from a isotropic Maxwellian
distribution unbound to the binary are ejected by the gravitational slingshot.
We construct a minimal, hybrid model for the depletion of the loss cone and the
orbital decay of the binary, and show that secondary slingshots - stars
returning on small impact parameter orbits to have a second super-elastic
scattering with the MBHB - may considerably help the shrinking of the pair in
the case of large binary mass ratios. In the absence of loss-cone refilling by
two-body relaxation or other processes, the mass ejected before the stalling of
a MBHB is half the binary reduced mass. About 50% of the ejected stars are
expelled ejected in a "burst" lasting ~1E4 yrs M_6^1/4, where M_6 is the binary
mass in units of 1E6 Msun. The loss cone is completely emptied in a few bulge
crossing timescales, 1E7 yrs M_6^1/4. Even in the absence of two-body
relaxation or gas dynamical processes, unequal mass and/or eccentric binaries
with M_6 >0.1 can shrink to the gravitational wave emission regime in less than
a Hubble time, and are therefore "safe" targets for the planned Laser
Interferometer Space Antenna (LISA).
