  We present exact solutions of test particle orbits spiralling inward from the
innermost stable circular orbit (ISCO) of a Kerr black hole. Our results are
valid for any allowed value of the angular momentum $a$-parameter of the Kerr
metric. These solutions are of considerable physical interest. In particular,
the radial 4-velocity of these orbits is both remarkably simple and, with the
radial coordinate scaled by its ISCO value, universal in form, otherwise
completely independent of the black hole spin.
