We describe a simple technique for optimizing the extraction of the forward-backward asymmetry ( A fb ) of Drell-Yan lepton pairs ( e + e − , μ + μ − ) produced in and pp collisions at hadron colliders. The method employs simple event weights which are functions of the rapidity and |cos  θ | decay angle of the lepton pair. It yields the best estimate of the acceptance corrected parton level ( ) forward backward asymmetry as a function of final state dilepton mass ( M ℓ ℓ ). Typically, when compared to the simple count method, the technique reduces the statistical errors by 20% for , and 40% for pp collisions, respectively. The method is equivalent to using the maximum likelihood method, but is much easier to implement. The technique can be used to search for new high mass and large width Z’ bosons which may be best detected through the observation of deviations from the Standard Model expectation for the forward-backward asymmetry. The technique can also be applied in the extraction of the foward-backward asymmetry in the production of top-antitop pairs.