  We describe a simple technique for optimizing the extraction of the
forward-backward asymmetry ($A_{fb}$) of Drell-Yan lepton pairs ($e^+e^-$,$
\mu^+\mu^-$) produced in $\bar{p}p$ and $pp$ collisions at hadron colliders.
The method employs simple event weights which are functions of the rapidity and
$cos\theta$ decay angle of the lepton pair. It yields the best estimate of the
acceptance corrected parton level ($\bar{q}q$) forward backward asymmetry as a
function of final state dilepton mass ($M_{\ell\ell}$). Typically, when
compared to the simple count method, the technique reduces the statistical
errors by 20% for $\bar{p}p$, and 40% for $pp$ collisions, respectively. 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. In addition, we
derive expressions for the QCD angular coefficients for Drell-Yan events.
