  We consider perturbations of a Schwarzschild black hole that can be of both
even and odd parity, keeping terms up to second order in perturbation theory,
for the $\ell=2$ axisymmetric case. We develop explicit formulae for the
evolution equations and radiated energies and waveforms using the
Regge-Wheeler-Zerilli approach. This formulation is useful, for instance, for
the treatment in the ``close limit approximation'' of the collision of
counterrotating black holes.
