  A compact stellar-mass object inspiralling onto a massive black hole deviates
from geodesic motion due to radiation-reaction forces as well as finite-size
effects. Such post-geodesic deviations need to be included with sufficient
precision into wave-form models for the upcoming space-based gravitational-wave
detector LISA. I present the formulation and solution of the Hamilton-Jacobi
equation of geodesics near Kerr black holes perturbed by the so-called
spin-curvature coupling, the leading order finite-size effect. In return, this
solution allows to compute a number of observables such as the turning points
of the orbits as well as the fundamental frequencies of motion. This result
provides one of the necessary ingredients for waveform models for LISA and an
important contribution useful for the relativistic two-body problem in general.
