  This article discusses the determination of asymmetries. We consider a sample
of events consisting of a peak of signal events on top of some background
events. Both signal and background have an unknown asymmetry, e.g. a spin or
forward-backward asymmetry. A method is proposed which determines signal and
background asymmetries simultaneously using event weighting. For vanishing
asymmetries the statistical error of the asymmetries reaches the minimal
variance bound (MVB) given by the Cram\'er-Rao inequality and it is very close
to it for large asymmetries. The method thus provides a significant gain in
statistics compared to the classical method of side band subtraction of
background asymmetries. It has the advantage with respect to the unbinned
maximum likelihood approach, reaching the MVB as well, that it does not require
loops over the event sample in the minimization procedure.
