Abstract: A small black hole orbiting a much larger one emits gravitational waves, loses energy and angular momentum, and slowly spirals inward. However, Einstein's Equivalence Principle implies that a small object ought to move along a free-fall geodesic of spacetime. Yet the effects of radiation reaction must have an influence on the object's motion. Careful theoretical analysis releases the apparent tension between the implications of the Equivalence Principle and of radiation-reaction, and shows how detailed calculations might be performed that will allow the Laser Interferometric Space Antenna, LISA, to track the evolution of extreme mass ratio binaries for thousands of orbits.