  Existing estimates of the gravitational-wave damping timescale of the
dominant quadrupole oscillation mode in the case of rapidly rotating stars are
based on using a Newtonian estimate for the energy of the mode, in combination
with the lowest-order post-Newtonian quadrupole formula for estimating the
gravitational-wave luminosity. We investigate a number of other choices for
estimating the gravitational-wave damping timescale in the nonrotating limit
and construct a highly accurate, empirically corrected formula that has a
maximum relative error of only 3% with respect to the perturbative result in
full general relativity. The expressions involved are sufficiently general to
be extended to the case of rapidly rotating stars. We also present a new
higher-order empirical relation for the gravitational-wave damping timescale of
quadrupole oscillations that is accurate in the whole range of expected values
for the compactness of neutron stars, without the need for involving the moment
of inertia.
