  In future measurements of the dilepton ($Z/\gamma^*$) transverse momentum,
\Qt, at both the Tevatron and LHC, the achievable bin widths and the ultimate
precision of the measurements will be limited by experimental resolution rather
than by the available event statistics. In a recent paper the variable \at,
which corresponds to the component of \Qt\ that is transverse to the dilepton
thrust axis, has been studied in this regard. In the region, \Qt\ $<$ 30 GeV,
\at\ has been shown to be less susceptible to experimental resolution and
efficiency effects than the \Qt. Extending over all \Qt, we now demonstrate
that dividing \at\ (or \Qt) by the measured dilepton invariant mass further
improves the resolution. In addition, we propose a new variable, \phistarEta,
that is determined exclusively from the measured lepton directions; this is
even more precisely determined experimentally than the above variables and is
similarly sensitive to the \Qt. The greater precision achievable using such
variables will enable more stringent tests of QCD and tighter constraints on
Monte Carlo event generator tunes.
