We 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. We 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 we compare its statistical power to that of a simple fit of the azimuthal distribution. In contrast to polarimetry with pair creation, for which we 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 %.Key words: Hard X-ray, gamma-ray, Compton scattering, polarimeter, polarisation asymmetry, optimal variable 1. Cosmic-source polarimetry: the high-energy frontier Polarimetry is a powerful diagnostic of specific phenomena at work in cosmic sources in the radio-wave and optical energy bands, but very few results are available at high photon energies: the only significant observation in the X-gamma energy range, to date, is the measurement of a linear polarisation fraction of P = 19 ± 1% of the 2.6 keV emission of the Crab nebula by a Bragg polarimeter on board . At higher energies, hard-X-ray and soft-gamma-ray telescopes that have flown to space in the past (COMPTEL