  I compute the average polarisation asymmetry from the Klein-Nishina
differential cross section on free electrons at rest. As expected from the
expression for the asymmetry, the average asymmetry is found to decrease like
the inverse of the incident photon energy asymptotically at high energy. I then
compute a simple estimator of the polarisation fraction that makes optimal use
of all the kinematic information present in an event final state, by the use of
"moments" method, and I compare its statistical power to that of a simple fit
of the azimuthal distribution. In contrast to polarimetry with pair creation,
for which I obtained an improvement by a factor of larger than two in a
previous work, here for Compton scattering the improvement is only of 10-20 %.
