  The gravitational radiation backreaction effects are considered in the
Lense-Thirring approximation. New methods for parameterizing the orbit and for
averaging the instantaneous radiative losses are developed. To first order in
the spin S of the black hole, both in the absence and in the presence of
gravitational radiation, a complete description of the test-particle orbit is
given. This is achieved by two improvements over the existing descriptions.
First, by introducing new angle variables with a straightforward geometrical
meaning. Second, by finding a new parametrization of a generic orbit, which
assures that the integration over a radial period can be done in an especially
simple way, by applying the residue theorem. The instantaneous radiation losses
of the system are computed using the formulation of Blanchet, Damour and
Iyer(1989). All losses are given both in terms of the dynamical constants of
motion and the properly defined orbital elements $a,e,\iota$ and $\Psi_0$. The
radiative losses of the constants characterizing the Lense-Thirring motion,
when suitably converted, are in agreement with earlier results of Kidder, Will
and Wiseman(1993), Ryan(1996) and Shibata(1994). In addition, the radiative
losses of two slowly changing orbital elements $\Psi_0,\Phi_0$ are given in
order to complete the characterization of the orbit.
