  The gravitational-wave energy flux produced during the head-on infall and
collision of two compact objects is calculated using two approaches: (i) a
post-Newtonian method, carried to second post-Newtonian order beyond the
quadrupole formula, valid for systems of arbitrary masses; and (ii) a
black-hole perturbation method, valid for a test-body falling radially toward a
black hole. In the test-body case, the methods are compared. The post-Newtonian
method is shown to converge to the ``exact'' perturbation result more slowly
than expected {\it a priori\/}. A surprisingly good approximation to the energy
radiated during the infall phase, as calculated by perturbation theory, is
found to be given by a Newtonian, or quadrupole, approximation combined with
the exact test-body equations of motion in the Schwarzschild spacetime.
